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breathe-horizontal" role="navigation" aria-label="pagination"> <a href="" class="pagination-previous is-invisible">Previous </a> <a href="/search/?searchtype=author&query=Le%2C+T+Q&start=50" class="pagination-next" >Next </a> <ul class="pagination-list"> <li> <a href="/search/?searchtype=author&query=Le%2C+T+Q&start=0" class="pagination-link is-current" aria-label="Goto page 1">1 </a> </li> <li> <a href="/search/?searchtype=author&query=Le%2C+T+Q&start=50" class="pagination-link " aria-label="Page 2" aria-current="page">2 </a> </li> </ul> </nav> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2411.02857">arXiv:2411.02857</a> <span> [<a href="https://arxiv.org/pdf/2411.02857">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Signal Processing">eess.SP</span> </div> </div> <p class="title is-5 mathjax"> Multi-Scale Temporal Analysis for Failure Prediction in Energy Systems </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Le%2C+A">Anh Le</a>, <a href="/search/?searchtype=author&query=Huynh%2C+P+K">Phat K. Huynh</a>, <a href="/search/?searchtype=author&query=Yadav%2C+O+P">Om P. Yadav</a>, <a href="/search/?searchtype=author&query=Le%2C+C">Chau Le</a>, <a href="/search/?searchtype=author&query=Pirim%2C+H">Harun Pirim</a>, <a href="/search/?searchtype=author&query=Le%2C+T+Q">Trung Q. Le</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2411.02857v1-abstract-short" style="display: inline;"> Many existing models struggle to predict nonlinear behavior during extreme weather conditions. This study proposes a multi-scale temporal analysis for failure prediction in energy systems using PMU data. The model integrates multi-scale analysis with machine learning to capture both short-term and long-term behavior. PMU data lacks labeled states despite logged failure records, making it difficult… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2411.02857v1-abstract-full').style.display = 'inline'; document.getElementById('2411.02857v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2411.02857v1-abstract-full" style="display: none;"> Many existing models struggle to predict nonlinear behavior during extreme weather conditions. This study proposes a multi-scale temporal analysis for failure prediction in energy systems using PMU data. The model integrates multi-scale analysis with machine learning to capture both short-term and long-term behavior. PMU data lacks labeled states despite logged failure records, making it difficult to distinguish between normal and disturbance conditions. We address this through: (1) Extracting domain features from PMU time series data; (2) Applying multi-scale windows (30s, 60s, 180s) for pattern detection; (3) Using Recursive Feature Elimination to identify key features; (4) Training multiple machine learning models. Key contributions: Identifying significant features across multi-scale windows; Demonstrating LightGBM's superior performance (0.896 precision); Showing multi-scale analysis outperforms single-window models (0.841). Our work focuses on weather-related failures, with plans to extend to equipment failure and lightning events. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2411.02857v1-abstract-full').style.display = 'none'; document.getElementById('2411.02857v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 5 November, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">6 pages, 3 figures, RAMS 2025</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2410.12027">arXiv:2410.12027</a> <span> [<a href="https://arxiv.org/pdf/2410.12027">pdf</a>, <a href="https://arxiv.org/format/2410.12027">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Fluid Dynamics">physics.flu-dyn</span> </div> </div> <p class="title is-5 mathjax"> Modal analysis of blood flows in saccular aneurysms </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Nguyen%2C+T">Thien-Tam Nguyen</a>, <a href="/search/?searchtype=author&query=Kasperski%2C+D">Davina Kasperski</a>, <a href="/search/?searchtype=author&query=Huynh%2C+P+K">Phat Kim Huynh</a>, <a href="/search/?searchtype=author&query=Le%2C+T+Q">Trung Quoc Le</a>, <a href="/search/?searchtype=author&query=Le%2C+T+B">Trung Bao Le</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2410.12027v1-abstract-short" style="display: inline;"> Currently, it is challenging to investigate aneurismal hemodynamics based on current in-vivo data such as Magnetic Resonance Imaging or Computed Tomography due to the limitations in both spatial and temporal resolutions. In this work, we investigate the use of modal analysis at various resolutions to examine its usefulness for analyzing blood flows in brain aneurysms. Two variants of Dynamic Mode… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.12027v1-abstract-full').style.display = 'inline'; document.getElementById('2410.12027v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2410.12027v1-abstract-full" style="display: none;"> Currently, it is challenging to investigate aneurismal hemodynamics based on current in-vivo data such as Magnetic Resonance Imaging or Computed Tomography due to the limitations in both spatial and temporal resolutions. In this work, we investigate the use of modal analysis at various resolutions to examine its usefulness for analyzing blood flows in brain aneurysms. Two variants of Dynamic Mode Decomposition (DMD): (i) Hankel-DMD; and (ii) Optimized-DMD, are used to extract the time-dependent dynamics of blood flows during one cardiac cycle. First, high-resolution hemodynamic data in patient-specific aneurysms are obtained using Computational Fluid Dynamics. Second, the dynamics modes, along with their spatial amplitudes and temporal magnitudes are calculated using the DMD analysis. Third, an examination of DMD analyses using a range of spatial and temporal resolutions of hemodynamic data to validate the applicability of DMD for low-resolution data, similar to ones in clinical practices. Our results show that DMD is able to characterize the inflow jet dynamics by separating large-scale structures and flow instabilities even at low spatial and temporal resolutions. Its robustness in quantifying the flow dynamics using the energy spectrum is demonstrated across different resolutions in all aneurysms in our study population. Our work indicates that DMD can be used for analyzing blood flow patterns of brain aneurysms and is a promising tool to be explored in in-vivo. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2410.12027v1-abstract-full').style.display = 'none'; document.getElementById('2410.12027v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 October, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2408.00239">arXiv:2408.00239</a> <span> [<a href="https://arxiv.org/pdf/2408.00239">pdf</a>, <a href="https://arxiv.org/format/2408.00239">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Astrophysics of Galaxies">astro-ph.GA</span> </div> </div> <p class="title is-5 mathjax"> Simulating intermediate black hole mass measurements for a sample of galaxies with nuclear star clusters using ELT/HARMONI high spatial resolution integral-field stellar kinematics </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Nguyen%2C+D+D">Dieu D. Nguyen</a>, <a href="/search/?searchtype=author&query=Cappellari%2C+M">Michele Cappellari</a>, <a href="/search/?searchtype=author&query=Ngo%2C+H+N">Hai N. Ngo</a>, <a href="/search/?searchtype=author&query=Le%2C+T+Q+T">Tinh Q. T. Le</a>, <a href="/search/?searchtype=author&query=Ho%2C+K+N+.+H">Khue N . H. Ho</a>, <a href="/search/?searchtype=author&query=Nguyen%2C+A+K">An K. Nguyen</a>, <a href="/search/?searchtype=author&query=Tong%2C+H+G+.">Huy G . Tong</a>, <a href="/search/?searchtype=author&query=On%2C+P+T">Phong T. On</a>, <a href="/search/?searchtype=author&query=Le%2C+T+N">Tuan N. Le</a>, <a href="/search/?searchtype=author&query=Pereira-Santaella%2C+M">Miguel Pereira-Santaella</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2408.00239v1-abstract-short" style="display: inline;"> The fraction of low-mass galaxies hosting an intermediate-mass black hole (IMBH, with masses $M_{\rm BH} \approx 10^2-10^5$ M$_\odot$), is sensitive to how black hole seeds formed in the early Universe but is observationally still unconstrained. In this paper, we assemble a sample of dwarf galaxies within 10 Mpc hosting bright nuclear star clusters (NSCs) that could host IMBHs. For a subset of the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.00239v1-abstract-full').style.display = 'inline'; document.getElementById('2408.00239v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2408.00239v1-abstract-full" style="display: none;"> The fraction of low-mass galaxies hosting an intermediate-mass black hole (IMBH, with masses $M_{\rm BH} \approx 10^2-10^5$ M$_\odot$), is sensitive to how black hole seeds formed in the early Universe but is observationally still unconstrained. In this paper, we assemble a sample of dwarf galaxies within 10 Mpc hosting bright nuclear star clusters (NSCs) that could host IMBHs. For a subset of them, we use their observed surface brightness from {\it Hubble Space Telescope} (\hst) images, an assumed synthetic spectrum of their stellar population, Jeans Anisotropic Model (JAM) of the stellar dynamics, and the {\tt HSIM} simulator software to create mock observations with the High Angular Resolution Monolithic Optical and Near-infrared Integral (HARMONI) field spectrograph for the Extremely Large Telescope (ELT). We analyze the simulated data cube like real data, using JAM to infer the IMBH mass and its error in a Bayesian framework. Our simulations show that the ELT/HARMONI instrument can clearly detect the existence of IMBH demographics in NSCs down to a mass of about 0.5\% of the NSC. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2408.00239v1-abstract-full').style.display = 'none'; document.getElementById('2408.00239v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 31 July, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">33 pages, 19 figures, 9 tables, submitted to MNRAS</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2407.13803">arXiv:2407.13803</a> <span> [<a href="https://arxiv.org/pdf/2407.13803">pdf</a>, <a href="https://arxiv.org/format/2407.13803">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Cryptography and Security">cs.CR</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Artificial Intelligence">cs.AI</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Computation and Language">cs.CL</span> </div> </div> <p class="title is-5 mathjax"> Less is More: Sparse Watermarking in LLMs with Enhanced Text Quality </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Hoang%2C+D+C">Duy C. Hoang</a>, <a href="/search/?searchtype=author&query=Le%2C+H+T+Q">Hung T. Q. Le</a>, <a href="/search/?searchtype=author&query=Chu%2C+R">Rui Chu</a>, <a href="/search/?searchtype=author&query=Li%2C+P">Ping Li</a>, <a href="/search/?searchtype=author&query=Zhao%2C+W">Weijie Zhao</a>, <a href="/search/?searchtype=author&query=Lao%2C+Y">Yingjie Lao</a>, <a href="/search/?searchtype=author&query=Doan%2C+K+D">Khoa D. Doan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2407.13803v1-abstract-short" style="display: inline;"> With the widespread adoption of Large Language Models (LLMs), concerns about potential misuse have emerged. To this end, watermarking has been adapted to LLM, enabling a simple and effective way to detect and monitor generated text. However, while the existing methods can differentiate between watermarked and unwatermarked text with high accuracy, they often face a trade-off between the quality of… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.13803v1-abstract-full').style.display = 'inline'; document.getElementById('2407.13803v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2407.13803v1-abstract-full" style="display: none;"> With the widespread adoption of Large Language Models (LLMs), concerns about potential misuse have emerged. To this end, watermarking has been adapted to LLM, enabling a simple and effective way to detect and monitor generated text. However, while the existing methods can differentiate between watermarked and unwatermarked text with high accuracy, they often face a trade-off between the quality of the generated text and the effectiveness of the watermarking process. In this work, we present a novel type of LLM watermark, Sparse Watermark, which aims to mitigate this trade-off by applying watermarks to a small subset of generated tokens distributed across the text. The key strategy involves anchoring watermarked tokens to words that have specific Part-of-Speech (POS) tags. Our experimental results demonstrate that the proposed watermarking scheme achieves high detectability while generating text that outperforms previous LLM watermarking methods in quality across various tasks <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.13803v1-abstract-full').style.display = 'none'; document.getElementById('2407.13803v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 17 July, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2407.01987">arXiv:2407.01987</a> <span> [<a href="https://arxiv.org/pdf/2407.01987">pdf</a>, <a href="https://arxiv.org/format/2407.01987">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Computer Vision and Pattern Recognition">cs.CV</span> </div> </div> <p class="title is-5 mathjax"> AHMsys: An Automated HVAC Modeling System for BIM Project </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Dang%2C+L+H">Long Hoang Dang</a>, <a href="/search/?searchtype=author&query=Nguyen%2C+D">Duy-Hung Nguyen</a>, <a href="/search/?searchtype=author&query=Le%2C+T+Q">Thai Quang Le</a>, <a href="/search/?searchtype=author&query=Nguyen%2C+T+T">Thinh Truong Nguyen</a>, <a href="/search/?searchtype=author&query=Mei%2C+C">Clark Mei</a>, <a href="/search/?searchtype=author&query=Hoang%2C+V">Vu Hoang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2407.01987v1-abstract-short" style="display: inline;"> This paper presents a novel system, named AHMsys, designed to automate the process of generating 3D Heating, Ventilation, and Air Conditioning (HVAC) models from 2D Computer-Aided Design (CAD) drawings, a key component of Building Information Modeling (BIM). By automatically preprocessing and extracting essential HVAC object information then creating detailed 3D models, our proposed AHMsys signifi… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.01987v1-abstract-full').style.display = 'inline'; document.getElementById('2407.01987v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2407.01987v1-abstract-full" style="display: none;"> This paper presents a novel system, named AHMsys, designed to automate the process of generating 3D Heating, Ventilation, and Air Conditioning (HVAC) models from 2D Computer-Aided Design (CAD) drawings, a key component of Building Information Modeling (BIM). By automatically preprocessing and extracting essential HVAC object information then creating detailed 3D models, our proposed AHMsys significantly reduced the 20 percent work schedule of the BIM process in Akila. This advancement highlights the essential impact of integrating AI technologies in managing the lifecycle of a digital representation of the building. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2407.01987v1-abstract-full').style.display = 'none'; document.getElementById('2407.01987v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 July, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2406.18602">arXiv:2406.18602</a> <span> [<a href="https://arxiv.org/pdf/2406.18602">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Applications">stat.AP</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Computation">stat.CO</span> </div> </div> <p class="title is-5 mathjax"> Multi-level Phenotypic Models of Cardiovascular Disease and Obstructive Sleep Apnea Comorbidities: A Longitudinal Wisconsin Sleep Cohort Study </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Nguyen%2C+D">Duy Nguyen</a>, <a href="/search/?searchtype=author&query=Hoang%2C+C">Ca Hoang</a>, <a href="/search/?searchtype=author&query=Huynh%2C+P+K">Phat K. Huynh</a>, <a href="/search/?searchtype=author&query=Truong%2C+T">Tien Truong</a>, <a href="/search/?searchtype=author&query=Nguyen%2C+D">Dang Nguyen</a>, <a href="/search/?searchtype=author&query=Sharma%2C+A">Abhay Sharma</a>, <a href="/search/?searchtype=author&query=Le%2C+T+Q">Trung Q. Le</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2406.18602v1-abstract-short" style="display: inline;"> Cardiovascular diseases (CVDs) are notably prevalent among patients with obstructive sleep apnea (OSA), posing unique challenges in predicting CVD progression due to the intricate interactions of comorbidities. Traditional models typically lack the necessary dynamic and longitudinal scope to accurately forecast CVD trajectories in OSA patients. This study introduces a novel multi-level phenotypic… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2406.18602v1-abstract-full').style.display = 'inline'; document.getElementById('2406.18602v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2406.18602v1-abstract-full" style="display: none;"> Cardiovascular diseases (CVDs) are notably prevalent among patients with obstructive sleep apnea (OSA), posing unique challenges in predicting CVD progression due to the intricate interactions of comorbidities. Traditional models typically lack the necessary dynamic and longitudinal scope to accurately forecast CVD trajectories in OSA patients. This study introduces a novel multi-level phenotypic model to analyze the progression and interplay of these conditions over time, utilizing data from the Wisconsin Sleep Cohort, which includes 1,123 participants followed for decades. Our methodology comprises three advanced steps: (1) Conducting feature importance analysis through tree-based models to underscore critical predictive variables like total cholesterol, low-density lipoprotein (LDL), and diabetes. (2) Developing a logistic mixed-effects model (LGMM) to track longitudinal transitions and pinpoint significant factors, which displayed a diagnostic accuracy of 0.9556. (3) Implementing t-distributed Stochastic Neighbor Embedding (t-SNE) alongside Gaussian Mixture Models (GMM) to segment patient data into distinct phenotypic clusters that reflect varied risk profiles and disease progression pathways. This phenotypic clustering revealed two main groups, with one showing a markedly increased risk of major adverse cardiovascular events (MACEs), underscored by the significant predictive role of nocturnal hypoxia and sympathetic nervous system activity from sleep data. Analysis of transitions and trajectories with t-SNE and GMM highlighted different progression rates within the cohort, with one cluster progressing more slowly towards severe CVD states than the other. This study offers a comprehensive understanding of the dynamic relationship between CVD and OSA, providing valuable tools for predicting disease onset and tailoring treatment approaches. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2406.18602v1-abstract-full').style.display = 'none'; document.getElementById('2406.18602v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 June, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">30 pages, 5 figure, 5 tables</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2403.01417">arXiv:2403.01417</a> <span> [<a href="https://arxiv.org/pdf/2403.01417">pdf</a>, <a href="https://arxiv.org/format/2403.01417">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Distributed, Parallel, and Cluster Computing">cs.DC</span> </div> </div> <p class="title is-5 mathjax"> Asyn2F: An Asynchronous Federated Learning Framework with Bidirectional Model Aggregation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Cao%2C+T">Tien-Dung Cao</a>, <a href="/search/?searchtype=author&query=Vuong%2C+N+T">Nguyen T. Vuong</a>, <a href="/search/?searchtype=author&query=Le%2C+T+Q">Thai Q. Le</a>, <a href="/search/?searchtype=author&query=Dao%2C+H+V+N">Hoang V. N. Dao</a>, <a href="/search/?searchtype=author&query=Truong-Huu%2C+T">Tram Truong-Huu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2403.01417v1-abstract-short" style="display: inline;"> In federated learning, the models can be trained synchronously or asynchronously. Many research works have focused on developing an aggregation method for the server to aggregate multiple local models into the global model with improved performance. They ignore the heterogeneity of the training workers, which causes the delay in the training of the local models, leading to the obsolete information… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.01417v1-abstract-full').style.display = 'inline'; document.getElementById('2403.01417v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2403.01417v1-abstract-full" style="display: none;"> In federated learning, the models can be trained synchronously or asynchronously. Many research works have focused on developing an aggregation method for the server to aggregate multiple local models into the global model with improved performance. They ignore the heterogeneity of the training workers, which causes the delay in the training of the local models, leading to the obsolete information issue. In this paper, we design and develop Asyn2F, an Asynchronous Federated learning Framework with bidirectional model aggregation. By bidirectional model aggregation, Asyn2F, on one hand, allows the server to asynchronously aggregate multiple local models and results in a new global model. On the other hand, it allows the training workers to aggregate the new version of the global model into the local model, which is being trained even in the middle of a training epoch. We develop Asyn2F considering the practical implementation requirements such as using cloud services for model storage and message queuing protocols for communications. Extensive experiments with different datasets show that the models trained by Asyn2F achieve higher performance compared to the state-of-the-art techniques. The experiments also demonstrate the effectiveness, practicality, and scalability of Asyn2F, making it ready for deployment in real scenarios. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2403.01417v1-abstract-full').style.display = 'none'; document.getElementById('2403.01417v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 March, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2024. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2311.00737">arXiv:2311.00737</a> <span> [<a href="https://arxiv.org/pdf/2311.00737">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Machine Learning">cs.LG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Instrumentation and Detectors">physics.ins-det</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Medical Physics">physics.med-ph</span> </div> </div> <p class="title is-5 mathjax"> Real-Time Magnetic Tracking and Diagnosis of COVID-19 via Machine Learning </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Nguyen%2C+D">Dang Nguyen</a>, <a href="/search/?searchtype=author&query=Huynh%2C+P+K">Phat K. Huynh</a>, <a href="/search/?searchtype=author&query=Bui%2C+V+D+A">Vinh Duc An Bui</a>, <a href="/search/?searchtype=author&query=Hwang%2C+K+Y">Kee Young Hwang</a>, <a href="/search/?searchtype=author&query=Jain%2C+N">Nityanand Jain</a>, <a href="/search/?searchtype=author&query=Nguyen%2C+C">Chau Nguyen</a>, <a href="/search/?searchtype=author&query=Minh%2C+L+H+N">Le Huu Nhat Minh</a>, <a href="/search/?searchtype=author&query=Van+Truong%2C+L">Le Van Truong</a>, <a href="/search/?searchtype=author&query=Nguyen%2C+X+T">Xuan Thanh Nguyen</a>, <a href="/search/?searchtype=author&query=Nguyen%2C+D+H">Dinh Hoang Nguyen</a>, <a href="/search/?searchtype=author&query=Dung%2C+L+T">Le Tien Dung</a>, <a href="/search/?searchtype=author&query=Le%2C+T+Q">Trung Q. Le</a>, <a href="/search/?searchtype=author&query=Phan%2C+M">Manh-Huong Phan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2311.00737v1-abstract-short" style="display: inline;"> The COVID-19 pandemic underscored the importance of reliable, noninvasive diagnostic tools for robust public health interventions. In this work, we fused magnetic respiratory sensing technology (MRST) with machine learning (ML) to create a diagnostic platform for real-time tracking and diagnosis of COVID-19 and other respiratory diseases. The MRST precisely captures breathing patterns through thre… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2311.00737v1-abstract-full').style.display = 'inline'; document.getElementById('2311.00737v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2311.00737v1-abstract-full" style="display: none;"> The COVID-19 pandemic underscored the importance of reliable, noninvasive diagnostic tools for robust public health interventions. In this work, we fused magnetic respiratory sensing technology (MRST) with machine learning (ML) to create a diagnostic platform for real-time tracking and diagnosis of COVID-19 and other respiratory diseases. The MRST precisely captures breathing patterns through three specific breath testing protocols: normal breath, holding breath, and deep breath. We collected breath data from both COVID-19 patients and healthy subjects in Vietnam using this platform, which then served to train and validate ML models. Our evaluation encompassed multiple ML algorithms, including support vector machines and deep learning models, assessing their ability to diagnose COVID-19. Our multi-model validation methodology ensures a thorough comparison and grants the adaptability to select the most optimal model, striking a balance between diagnostic precision with model interpretability. The findings highlight the exceptional potential of our diagnostic tool in pinpointing respiratory anomalies, achieving over 90% accuracy. This innovative sensor technology can be seamlessly integrated into healthcare settings for patient monitoring, marking a significant enhancement for the healthcare infrastructure. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2311.00737v1-abstract-full').style.display = 'none'; document.getElementById('2311.00737v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 1 November, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2307.09135">arXiv:2307.09135</a> <span> [<a href="https://arxiv.org/pdf/2307.09135">pdf</a>, <a href="https://arxiv.org/ps/2307.09135">ps</a>, <a href="https://arxiv.org/format/2307.09135">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Number Theory">math.NT</span> </div> </div> <p class="title is-5 mathjax"> From 3-dimensional skein theory to functions near Q </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Garoufalidis%2C+S">Stavros Garoufalidis</a>, <a href="/search/?searchtype=author&query=Le%2C+T+T+T+Q">Thang T. T. Q. Le</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2307.09135v2-abstract-short" style="display: inline;"> Motivated by the Quantum Modularity Conjecture and its arithmetic aspects related to the Habiro ring of a number field, we define a map from the Kauffman bracket skein module of an integer homology 3-sphere to the Habiro ring, and use Witten's conjecture (now a theorem) to show that the image is an effectively computable module of finite rank that can be used to phrase the quantum modularity conje… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2307.09135v2-abstract-full').style.display = 'inline'; document.getElementById('2307.09135v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2307.09135v2-abstract-full" style="display: none;"> Motivated by the Quantum Modularity Conjecture and its arithmetic aspects related to the Habiro ring of a number field, we define a map from the Kauffman bracket skein module of an integer homology 3-sphere to the Habiro ring, and use Witten's conjecture (now a theorem) to show that the image is an effectively computable module of finite rank that can be used to phrase the quantum modularity conjecture. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2307.09135v2-abstract-full').style.display = 'none'; document.getElementById('2307.09135v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 August, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 18 July, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">15 pages, 4 figures. Updated 2 references</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2304.10085">arXiv:2304.10085</a> <span> [<a href="https://arxiv.org/pdf/2304.10085">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Medical Physics">physics.med-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Biological Physics">physics.bio-ph</span> </div> </div> <p class="title is-5 mathjax"> Multifractality in Surface Potential for Cancer Diagnosis </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Huynh%2C+P+K">Phat K. Huynh</a>, <a href="/search/?searchtype=author&query=Nguyen%2C+D">Dang Nguyen</a>, <a href="/search/?searchtype=author&query=Binder%2C+G">Grace Binder</a>, <a href="/search/?searchtype=author&query=Ambardar%2C+S">Sharad Ambardar</a>, <a href="/search/?searchtype=author&query=Le%2C+T+Q">Trung Q. Le</a>, <a href="/search/?searchtype=author&query=Voronine%2C+D+V">Dmitri V. Voronine</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2304.10085v1-abstract-short" style="display: inline;"> Recent advances in high-resolution biomedical imaging focusing on morphological, electrical, and biochemical properties of cells and tissues, scaling from cell clusters down to the molecular level, have improved cancer diagnosis. Multiscale imaging revealed high complexity that requires advanced data processing methods of multifractal analysis. We performed label-free multiscale imaging of surface… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2304.10085v1-abstract-full').style.display = 'inline'; document.getElementById('2304.10085v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2304.10085v1-abstract-full" style="display: none;"> Recent advances in high-resolution biomedical imaging focusing on morphological, electrical, and biochemical properties of cells and tissues, scaling from cell clusters down to the molecular level, have improved cancer diagnosis. Multiscale imaging revealed high complexity that requires advanced data processing methods of multifractal analysis. We performed label-free multiscale imaging of surface potential variations in human ovarian and breast cancer cells using Kelvin probe force microscopy (KPFM). An improvement in the differentiation between normal and cancerous cells of for multifractal analysis using adaptive versus median threshold for image binarization was demonstrated. The results reveal the potential of using multifractality as a new biomarker for cancer diagnosis. Furthermore, the surface potential imaging can be used in combination with morphological imaging for cancer diagnosis. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2304.10085v1-abstract-full').style.display = 'none'; document.getElementById('2304.10085v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 April, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">35 pages, 11 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2303.08082">arXiv:2303.08082</a> <span> [<a href="https://arxiv.org/pdf/2303.08082">pdf</a>, <a href="https://arxiv.org/ps/2303.08082">ps</a>, <a href="https://arxiv.org/format/2303.08082">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> </div> </div> <p class="title is-5 mathjax"> Quantum traces for $SL_n$-skein algebras </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=L%C3%AA%2C+T+T+Q">Thang T. Q. L锚</a>, <a href="/search/?searchtype=author&query=Yu%2C+T">Tao Yu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2303.08082v1-abstract-short" style="display: inline;"> We establish the existence of several quantum trace maps. The simplest one is an algebra map between two quantizations of the algebra of regular functions on the $SL_n$-character variety of a surface $\mathfrak{S}$ equipped with an ideal triangulation $位$. The first is the (stated) $SL_n$-skein algebra $\mathscr{S}(\mathfrak{S})$. The second $\overline{\mathcal{X}}(\mathfrak{S},位)$ is the Fock and… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.08082v1-abstract-full').style.display = 'inline'; document.getElementById('2303.08082v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2303.08082v1-abstract-full" style="display: none;"> We establish the existence of several quantum trace maps. The simplest one is an algebra map between two quantizations of the algebra of regular functions on the $SL_n$-character variety of a surface $\mathfrak{S}$ equipped with an ideal triangulation $位$. The first is the (stated) $SL_n$-skein algebra $\mathscr{S}(\mathfrak{S})$. The second $\overline{\mathcal{X}}(\mathfrak{S},位)$ is the Fock and Goncharov's quantization of their $X$-moduli space. The quantum trace is an algebra homomorphism $\bar{tr}^X:\overline{\mathscr{S}}(\mathfrak{S})\to\overline{\mathcal{X}}(\mathfrak{S},位)$ where the reduced skein algebra $\overline{\mathscr{S}}(\mathfrak{S})$ is a quotient of $\mathscr{S}(\mathfrak{S})$. When the quantum parameter is 1, the quantum trace $\bar{tr}^X$ coincides with the classical Fock-Goncharov homomorphism. This is a generalization of the Bonahon-Wong quantum trace map for the case $n=2$. We then define the extended Fock-Goncharov algebra $\mathcal{X}(\mathfrak{S},位)$ and show that $\bar{tr}^X$ can be lifted to $tr^X:\mathscr{S}(\mathfrak{S})\to\mathcal{X}(\mathfrak{S},位)$. We show that both $\bar{tr}^X$ and $tr^X$ are natural with respect to the change of triangulations. When each connected component of $\mathfrak{S}$ has non-empty boundary and no interior ideal point, we define a quantization of the Fock-Goncharov $A$-moduli space $\overline{\mathcal{A}}(\mathfrak{S},位)$ and its extension $\mathcal{A}(\mathfrak{S},位)$. We then show that there exist quantum traces $\bar{tr}^A:\overline{\mathscr{S}}(\mathfrak{S})\to\overline{\mathcal{A}}(\mathfrak{S},位)$ and $tr^A:\mathscr{S}(\mathfrak{S})\hookrightarrow\mathcal{A}(\mathfrak{S},位)$, where the second map is injective, while the first is injective at least when $\mathfrak{S}$ is a polygon. They are equivalent to the $X$-versions but have better algebraic properties. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.08082v1-abstract-full').style.display = 'none'; document.getElementById('2303.08082v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 March, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">111 pages, 35 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57N10; 57M25 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2206.10906">arXiv:2206.10906</a> <span> [<a href="https://arxiv.org/pdf/2206.10906">pdf</a>, <a href="https://arxiv.org/format/2206.10906">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> </div> <p class="title is-5 mathjax"> Stated skein modules of 3-manifolds and TQFT </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Costantino%2C+F">Francesco Costantino</a>, <a href="/search/?searchtype=author&query=Le%2C+T+T+Q">Thang T. Q. Le</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2206.10906v1-abstract-short" style="display: inline;"> We study the behaviour of the Kauffman bracket skein modules of 3-manifolds under gluing along surfaces. For this purpose we extend the notion of Kauffman bracket skein modules to $3$-manifolds with marking consisting of open intervals and circles in the boundary. The new module is called the stated skein module. The first main results concern non-injectivity of certain natural maps defined when… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2206.10906v1-abstract-full').style.display = 'inline'; document.getElementById('2206.10906v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2206.10906v1-abstract-full" style="display: none;"> We study the behaviour of the Kauffman bracket skein modules of 3-manifolds under gluing along surfaces. For this purpose we extend the notion of Kauffman bracket skein modules to $3$-manifolds with marking consisting of open intervals and circles in the boundary. The new module is called the stated skein module. The first main results concern non-injectivity of certain natural maps defined when forming connected sums along a sphere or along a closed disk. These maps are injective for surfaces, or for generic quantum parameter, but we show that in general they are not injective when the quantum parameter is a root of 1. The result applies to the classical skein modules as well. A particular interesting result is that when the quantum parameter is a root of 1, the empty skein is zero in a connected sum where each constituent manifold has non-empty marking. We also prove various non injectivity results for the Chebyshev-Frobenius map and the natural map induced by the deletion of marked balls. We then consider the general case of gluing along a surface, showing that the stated skein module can be interpreted as a monoidal symmetric functor from a category of "decorated cobordisms" to a Morita category of algebras and their bimodules. We apply this result to deduce several properties of stated skein modules as a Van-Kampen like theorem as well as a computation through Heegaard decompositions and a relation to Hochshild homology for trivial circle bundles over surfaces. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2206.10906v1-abstract-full').style.display = 'none'; document.getElementById('2206.10906v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 June, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">37 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> Primary 57N10; Secondary: 57M25 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2202.12430">arXiv:2202.12430</a> <span> [<a href="https://arxiv.org/pdf/2202.12430">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Systems and Control">eess.SY</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Chaotic Dynamics">nlin.CD</span> </div> </div> <p class="title is-5 mathjax"> Koopman Spectral Analysis of Intermittent Dynamics in Complex Systems: A Case Study in Pathophysiological Processes of Obstructive Sleep Apnea </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Huynh%2C+P+K">Phat K. Huynh</a>, <a href="/search/?searchtype=author&query=Setty%2C+A+R">Arveity R. Setty</a>, <a href="/search/?searchtype=author&query=Le%2C+T+Q">Trung Q. Le</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2202.12430v1-abstract-short" style="display: inline;"> Complex systems, such as pathophysiological processes, commonly exhibit chaotic, nonlinear, and intermittent phenomena. Koopman operator theory and Hankel alternative view of Koopman (HAVOK) model have been widely used to decompose the chaos of the complex system dynamics into an intermittent forced linear system. Although the statistics of the intermittent forcing have been proposed to characteri… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2202.12430v1-abstract-full').style.display = 'inline'; document.getElementById('2202.12430v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2202.12430v1-abstract-full" style="display: none;"> Complex systems, such as pathophysiological processes, commonly exhibit chaotic, nonlinear, and intermittent phenomena. Koopman operator theory and Hankel alternative view of Koopman (HAVOK) model have been widely used to decompose the chaos of the complex system dynamics into an intermittent forced linear system. Although the statistics of the intermittent forcing have been proposed to characterize intermittencies in the HAVOK model, they were not adequate to attribute for the mode switching of nonlinear dynamics and the fat-tailed non-Gaussian distribution originated from high-frequency bursts and rarely-observed intermittent forcing. The paper proposed a new intermittency dynamics analysis approach to characterize the intermittent phases, chaotic bursts, and local spectral-temporal properties of various intermittent dynamics modes using spectral decomposition and wavelet analysis. To validate our methods, the intermittency behavior of apneic events in obstructive sleep apnea disorder was selected as the case, in which heart rate variability (HRV) features were extracted. Next, we constructed the Hankel matrix from the HRV features and obtained the last eigen time-delay coordinate by singular value decomposition of the Hankel matrix, which was modeled as an intermittent forcing input. The statistics of the forcing in OSA demonstrated the fat-tailed distribution of the intermittent forcing, which correspond to the intermittency of the underlying OSA pathophysiological process. The pooled means and standard deviations of the burst duration and the inter-burst duration across OSA patients were also calculated to be minutes and minutes. Scalogram amplitude and spectral decomposition of the wavelet transform exhibited various predominant frequencies and dynamics modes associated with apneic events. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2202.12430v1-abstract-full').style.display = 'none'; document.getElementById('2202.12430v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 February, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">28 pages, 9 figures, 1 table</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2201.00045">arXiv:2201.00045</a> <span> [<a href="https://arxiv.org/pdf/2201.00045">pdf</a>, <a href="https://arxiv.org/format/2201.00045">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> </div> </div> <p class="title is-5 mathjax"> Stated SL(n)-Skein Modules and Algebras </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=L%C3%AA%2C+T+T+Q">Thang T. Q. L锚</a>, <a href="/search/?searchtype=author&query=Sikora%2C+A+S">Adam S. Sikora</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2201.00045v3-abstract-short" style="display: inline;"> We develop a theory of stated SL(n)-skein modules, $S_n(M,N),$ of 3-manifolds $M$ marked with intervals $N$ in their boundaries. They consist of linear combinations of $n$-webs with ends in $N$, considered up to skein relations inspired by the relations of the Reshetikhin-Turaev theory. We prove that cutting $M$ along a disk resulting in a $3$-manifold $M'$ yields a homomorphism… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2201.00045v3-abstract-full').style.display = 'inline'; document.getElementById('2201.00045v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2201.00045v3-abstract-full" style="display: none;"> We develop a theory of stated SL(n)-skein modules, $S_n(M,N),$ of 3-manifolds $M$ marked with intervals $N$ in their boundaries. They consist of linear combinations of $n$-webs with ends in $N$, considered up to skein relations inspired by the relations of the Reshetikhin-Turaev theory. We prove that cutting $M$ along a disk resulting in a $3$-manifold $M'$ yields a homomorphism $S_n(M)\to S_n(M')$. That result allows to analyze the skein modules of $3$-manifolds through the skein modules of their pieces. The theory of stated skein modules is particularly rich for thickened surfaces $M=危\times (-1,1),$ in whose case, $S_n(M)$ is an algebra, denoted by $S_n(危).$ We prove that the skein algebra of the ideal bigon is $O_q(SL(n))$ and that it provides simple geometric interpretations of the product, coproduct, counit, the antipode, and the cobraided structure on $O_q(SL(n)).$ Additionally, we show that a splitting of a thickened bigon near a marking defines a $O_q(SL(n))$-comodule structure on $S_n(M),$ or dually, an $U_q(sl_n)$-module structure. Furthermore, we show that the skein algebra of surfaces $危_1, 危_2$ glued along two sides of a triangle is isomorphic with the braided tensor product $S_n(危_1)\underline{\otimes} S_n(危_2)$ of Majid. These results allow for a geometric interpretation of further concepts in the theory of quantum groups, for example, of the braided products and of Majid's transmutation operation. We prove that the factorization homology of surfaces with coefficients in $Rep\, U_q(sl_n)$ is equivalent to the category of left modules over $S_n(危)$. We also discuss the relation with the quantum moduli spaces of Alekseev-Schomerus. Finally, we show that for surfaces $危$ with boundary, $S_n(危)$ is a free module with a basis induced from the Kashiwara-Lusztig canonical bases. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2201.00045v3-abstract-full').style.display = 'none'; document.getElementById('2201.00045v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 8 June, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 31 December, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">85 pages, many figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57K3; 57K16; 20G42; 17B37 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2111.05761">arXiv:2111.05761</a> <span> [<a href="https://arxiv.org/pdf/2111.05761">pdf</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Applications">stat.AP</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Signal Processing">eess.SP</span> </div> </div> <p class="title is-5 mathjax"> A Probabilistic Domain-knowledge Framework for Nosocomial Infection Risk Estimation of Communicable Viral Diseases in Healthcare Personnel: A Case Study for COVID-19 </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Huynh%2C+P+K">Phat K. Huynh</a>, <a href="/search/?searchtype=author&query=Setty%2C+A+R">Arveity R. Setty</a>, <a href="/search/?searchtype=author&query=Yadav%2C+O+P">Om P. Yadav</a>, <a href="/search/?searchtype=author&query=Le%2C+T+Q">Trung Q. Le</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2111.05761v1-abstract-short" style="display: inline;"> Hospital-acquired infections of communicable viral diseases (CVDs) are posing a tremendous challenge to healthcare workers globally. Healthcare personnel (HCP) is facing a consistent risk of hospital-acquired infections, and subsequently higher rates of morbidity and mortality. We proposed a domain knowledge-driven infection risk model to quantify the individual HCP and the population-level health… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.05761v1-abstract-full').style.display = 'inline'; document.getElementById('2111.05761v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2111.05761v1-abstract-full" style="display: none;"> Hospital-acquired infections of communicable viral diseases (CVDs) are posing a tremendous challenge to healthcare workers globally. Healthcare personnel (HCP) is facing a consistent risk of hospital-acquired infections, and subsequently higher rates of morbidity and mortality. We proposed a domain knowledge-driven infection risk model to quantify the individual HCP and the population-level healthcare facility risks. For individual-level risk estimation, a time-variant infection risk model is proposed to capture the transmission dynamics of CVDs. At the population-level, the infection risk is estimated using a Bayesian network model constructed from three feature sets including individual-level factors, engineering control factors, and administrative control factors. The sensitivity analyses indicated that the uncertainty in the individual infection risk can be attributed to two variables: the number of close contacts and the viral transmission probability. The model validation was implemented in the transmission probability model, individual level risk model, and population-level risk model using a Coronavirus disease case study. Regarding the first, multivariate logistic regression was applied for a cross-sectional data in the UK with an AIC value of 7317.70 and a 10-fold cross validation accuracy of 78.23%. For the second model, we collected laboratory-confirmed COVID-19 cases of HCP in different occupations. The occupation-specific risk evaluation suggested the highest-risk occupations were registered nurses, medical assistants, and respiratory therapists, with estimated risks of 0.0189, 0.0188, and 0.0176, respectively. To validate the population-level risk model, the infection risk in Texas and California was estimated. The proposed model will significantly influence the PPE allocation and safety plans for HCP <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.05761v1-abstract-full').style.display = 'none'; document.getElementById('2111.05761v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 4 November, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">10 pages, 4 figures, Journal of Biomedical and Health Informatics</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2107.11926">arXiv:2107.11926</a> <span> [<a href="https://arxiv.org/pdf/2107.11926">pdf</a>, <a href="https://arxiv.org/ps/2107.11926">ps</a>, <a href="https://arxiv.org/format/2107.11926">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Rings and Algebras">math.RA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Representation Theory">math.RT</span> </div> </div> <p class="title is-5 mathjax"> Root of unity quantum cluster algebras and Cayley-Hamilton algebras </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Huang%2C+S">Shengnan Huang</a>, <a href="/search/?searchtype=author&query=L%C3%AA%2C+T+T+Q">Thang T. Q. L锚</a>, <a href="/search/?searchtype=author&query=Yakimov%2C+M">Milen Yakimov</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2107.11926v3-abstract-short" style="display: inline;"> We prove that large classes of algebras in the framework of root of unity quantum cluster algebras have the structures of maximal orders in central simple algebras and Cayley-Hamilton algebras in the sense of Procesi. We show that every root of unity upper quantum cluster algebra is a maximal order and obtain an explicit formula for its reduced trace. Under mild assumptions, inside each such algeb… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2107.11926v3-abstract-full').style.display = 'inline'; document.getElementById('2107.11926v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2107.11926v3-abstract-full" style="display: none;"> We prove that large classes of algebras in the framework of root of unity quantum cluster algebras have the structures of maximal orders in central simple algebras and Cayley-Hamilton algebras in the sense of Procesi. We show that every root of unity upper quantum cluster algebra is a maximal order and obtain an explicit formula for its reduced trace. Under mild assumptions, inside each such algebra we construct a canonical central subalgebra isomorphic to the underlying upper cluster algebra, such that the pair is a Cayley-Hamilton algebra; its fully Azumaya locus is shown to contain a copy of the underlying cluster $\mathcal{A}$-variety. Both results are proved in the wider generality of intersections of mixed quantum tori over subcollections of seeds. Furthermore, we prove that all monomial subalgebras of root of unity quantum tori are Cayley-Hamilton algebras and classify those ones that are maximal orders. Arbitrary intersections of those over subsets of seeds are also proved to be Cayley-Hamilton algebras. Previous approaches to constructing maximal orders relied on filtration and homological methods. We use new methods based on cluster algebras. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2107.11926v3-abstract-full').style.display = 'none'; document.getElementById('2107.11926v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 5 January, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 25 July, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 13F60 (Primary) 16G30; 17B37; 14A22 (Secondary) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2103.11532">arXiv:2103.11532</a> <span> [<a href="https://arxiv.org/pdf/2103.11532">pdf</a>, <a href="https://arxiv.org/ps/2103.11532">ps</a>, <a href="https://arxiv.org/format/2103.11532">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> </div> </div> <p class="title is-5 mathjax"> Faithfullness of geometric action of skein algebras </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Le%2C+T+T+Q">Thang T. Q. Le</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2103.11532v1-abstract-short" style="display: inline;"> We show that the action of the Kauffman bracket skein algebra of a surface $危$ on the skein module of the handlebody bounded by $危$ is faithful if and only if the quantum parameter is not a root of 1. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2103.11532v1-abstract-full" style="display: none;"> We show that the action of the Kauffman bracket skein algebra of a surface $危$ on the skein module of the handlebody bounded by $危$ is faithful if and only if the quantum parameter is not a root of 1. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.11532v1-abstract-full').style.display = 'none'; document.getElementById('2103.11532v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 March, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">13 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57N10; 57M25 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2012.15272">arXiv:2012.15272</a> <span> [<a href="https://arxiv.org/pdf/2012.15272">pdf</a>, <a href="https://arxiv.org/format/2012.15272">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> </div> </div> <p class="title is-5 mathjax"> Quantum traces and embeddings of stated skein algebras into quantum tori </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=L%C3%AA%2C+T+T+Q">Thang T. Q. L锚</a>, <a href="/search/?searchtype=author&query=Yu%2C+T">Tao Yu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2012.15272v1-abstract-short" style="display: inline;"> The stated skein algebra of a punctured bordered surface (or equivalently, a marked surface) is a generalization of the well-known Kauffman bracket skein algebra of unmarked surfaces and can be considered as an extension of the quantum special linear group $\mathcal{O}_{q^2}(SL_2)$ from a bigon to general surfaces. We show that the stated skein algebra of a punctured bordered surface with non-empt… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2012.15272v1-abstract-full').style.display = 'inline'; document.getElementById('2012.15272v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2012.15272v1-abstract-full" style="display: none;"> The stated skein algebra of a punctured bordered surface (or equivalently, a marked surface) is a generalization of the well-known Kauffman bracket skein algebra of unmarked surfaces and can be considered as an extension of the quantum special linear group $\mathcal{O}_{q^2}(SL_2)$ from a bigon to general surfaces. We show that the stated skein algebra of a punctured bordered surface with non-empty boundary can be embedded into quantum tori in two different ways. The first embedding can be considered as a quantization of the map expressing the trace of a closed curve in terms of the shear coordinates of the enhanced Teichm眉ller space, and is a lift of Bonahon-Wong's quantum trace map. The second embedding can be considered as a quantization of the map expresses the trace of a closed curve in terms of the lambda length coordinates of the decorated Teichm眉ller space, and is an extension of Muller's quantum trace map. We explain the relation between the two quantum trace maps. We also show that the quantum cluster algebra of Muller is equal to a reduced version of the stated skein algebra. As applications we show that the stated skein algebra is an orderly finitely generated Noetherian domain and calculate its Gelfand-Kirillov dimension. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2012.15272v1-abstract-full').style.display = 'none'; document.getElementById('2012.15272v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 December, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">40 pages, 10 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57N10; 57M25 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2011.02130">arXiv:2011.02130</a> <span> [<a href="https://arxiv.org/pdf/2011.02130">pdf</a>, <a href="https://arxiv.org/format/2011.02130">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> </div> <p class="title is-5 mathjax"> The Chebyshev-Frobenius homomorphism for stated skein modules of 3-manifolds </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Bloomquist%2C+W">Wade Bloomquist</a>, <a href="/search/?searchtype=author&query=L%C3%AA%2C+T+T+Q">Thang T. Q. L锚</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2011.02130v2-abstract-short" style="display: inline;"> We study the stated skein modules of marked 3-manifolds. We generalize the splitting homomorphism for stated skein algebras of surfaces to a splitting homomorphism for stated skein modules of 3-manifolds. We show that there exists a Chebyshev-Frobenius homomorphism for the stated skein modules of 3-manifolds which extends the Chebyshev homomorphism of the skein algebras of unmarked surfaces origin… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2011.02130v2-abstract-full').style.display = 'inline'; document.getElementById('2011.02130v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2011.02130v2-abstract-full" style="display: none;"> We study the stated skein modules of marked 3-manifolds. We generalize the splitting homomorphism for stated skein algebras of surfaces to a splitting homomorphism for stated skein modules of 3-manifolds. We show that there exists a Chebyshev-Frobenius homomorphism for the stated skein modules of 3-manifolds which extends the Chebyshev homomorphism of the skein algebras of unmarked surfaces originally constructed by Bonahon and Wong. Additionally, we show that the Chebyshev-Frobenius map commutes with the splitting homomorphism. This is then used to show that in the case of the stated skein algebra of a surface, the Chebyshev-Frobenius map is the unique extension of the dual Frobenius map (in the sense of Lusztig) of $\mathcal{O}_{q^2}(SL(2))$ through the triangular decomposition afforded by an ideal triangulation of the surface. In particular, this gives a skein theoretic construction of the Hopf dual of Lusztig's Frobenius homomorphism. A second conceptual framework is given, which shows that the Chebyshev-Frobenius homomorphism for the stated skein algebra of a surface is the unique restriction of the Frobenius homomorphism of quantum tori through the quantum trace map. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2011.02130v2-abstract-full').style.display = 'none'; document.getElementById('2011.02130v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 November, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 4 November, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">44 pages, 27 figures; Additional references added</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57N10 (Primary); 57M25 (Secondary) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2005.14577">arXiv:2005.14577</a> <span> [<a href="https://arxiv.org/pdf/2005.14577">pdf</a>, <a href="https://arxiv.org/ps/2005.14577">ps</a>, <a href="https://arxiv.org/format/2005.14577">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> </div> </div> <p class="title is-5 mathjax"> Stated skein modules of marked 3-manifolds/surfaces, a survey </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=L%C3%AA%2C+T+T+Q">Thang T. Q. L锚</a>, <a href="/search/?searchtype=author&query=Yu%2C+T">Tao Yu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2005.14577v1-abstract-short" style="display: inline;"> We give a survey of some old and new results about the stated skein modules/algebras of 3-manifolds/surfaces. For generic quantum parameter, we discuss the splitting homomorphism for the 3-manifold case, general structures of the stated skein algebras of marked surfaces (or bordered punctured surfaces) and their embeddings into quantum tori. For roots of 1 quantum parameter, we discuss the Frobeni… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2005.14577v1-abstract-full').style.display = 'inline'; document.getElementById('2005.14577v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2005.14577v1-abstract-full" style="display: none;"> We give a survey of some old and new results about the stated skein modules/algebras of 3-manifolds/surfaces. For generic quantum parameter, we discuss the splitting homomorphism for the 3-manifold case, general structures of the stated skein algebras of marked surfaces (or bordered punctured surfaces) and their embeddings into quantum tori. For roots of 1 quantum parameter, we discuss the Frobenius homomorphism (for both marked 3-manifolds and marked surfaces), describe the center of the skein algebra of marked surfaces, the dimension of the skein algebra over the center, and the representation theory of the skein algebra. In particular, we show that the skein algebra of non-closed marked surface at any root of 1 is a maximal order. We give a full description of the Azumaya locus of the skein algebra of the puncture torus and give partial results for closed surfaces. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2005.14577v1-abstract-full').style.display = 'none'; document.getElementById('2005.14577v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 29 May, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">22 pages, 6 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57N10; 57M25 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1908.05775">arXiv:1908.05775</a> <span> [<a href="https://arxiv.org/pdf/1908.05775">pdf</a>, <a href="https://arxiv.org/ps/1908.05775">ps</a>, <a href="https://arxiv.org/format/1908.05775">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> </div> </div> <p class="title is-5 mathjax"> Lower and Upper Bounds for Positive Bases of Skein Algebras </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=L%C3%AA%2C+T+T+Q">Thang T. Q. L锚</a>, <a href="/search/?searchtype=author&query=Thurston%2C+D+P">Dylan P. Thurston</a>, <a href="/search/?searchtype=author&query=Yu%2C+T">Tao Yu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1908.05775v1-abstract-short" style="display: inline;"> We show that the if a sequence of normalized polynomials gives rise to a positive basis of the skein algebra of a surface, then it is sandwiched between the two types of Chebyshev polynomials. For the closed torus, we show that the normalized sequence of Chebyshev polynomials of type one $(\hat{T}_n)$ is the only one which gives a positive basis. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1908.05775v1-abstract-full" style="display: none;"> We show that the if a sequence of normalized polynomials gives rise to a positive basis of the skein algebra of a surface, then it is sandwiched between the two types of Chebyshev polynomials. For the closed torus, we show that the normalized sequence of Chebyshev polynomials of type one $(\hat{T}_n)$ is the only one which gives a positive basis. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1908.05775v1-abstract-full').style.display = 'none'; document.getElementById('1908.05775v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 August, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">12 pages, 5 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57N10; 57M25 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1907.11400">arXiv:1907.11400</a> <span> [<a href="https://arxiv.org/pdf/1907.11400">pdf</a>, <a href="https://arxiv.org/format/1907.11400">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> </div> </div> <p class="title is-5 mathjax"> Stated skein algebras of surfaces </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Costantino%2C+F">Francesco Costantino</a>, <a href="/search/?searchtype=author&query=Le%2C+T+T+Q">Thang T. Q. Le</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1907.11400v2-abstract-short" style="display: inline;"> We study the algebraic and geometric properties of stated skein algebras of surfaces with punctured boundary. We prove that the skein algebra of the bigon is isomorphic to the quantum group ${\mathcal O}_{q^2}(\mathrm{SL}(2))$ providing a topological interpretation for its structure morphisms. We also show that its stated skein algebra lifts in a suitable sense the Reshetikhin-Turaev functor and i… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1907.11400v2-abstract-full').style.display = 'inline'; document.getElementById('1907.11400v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1907.11400v2-abstract-full" style="display: none;"> We study the algebraic and geometric properties of stated skein algebras of surfaces with punctured boundary. We prove that the skein algebra of the bigon is isomorphic to the quantum group ${\mathcal O}_{q^2}(\mathrm{SL}(2))$ providing a topological interpretation for its structure morphisms. We also show that its stated skein algebra lifts in a suitable sense the Reshetikhin-Turaev functor and in particular we recover the dual $R$-matrix for ${\mathcal O}_{q^2}(\mathrm{SL}(2))$ in a topological way. We deduce that the skein algebra of a surface with $n$ boundary components is an algebra-comodule over ${\mathcal O}_{q^2}(\mathrm{SL}(2))^{\otimes{n}}$ and prove that cutting along an ideal arc corresponds to Hochshild cohomology of bicomodules. We give a topological interpretation of braided tensor product of stated skein algebras of surfaces as "glueing on a triangle"; then we recover topologically some braided bialgebras in the category of ${\mathcal O}_{q^2}(\mathrm{SL}(2))$-comodules, among which the "transmutation" of ${\mathcal O}_{q^2}(\mathrm{SL}(2))$. We also provide an operadic interpretation of stated skein algebras as an example of a "geometric non symmetric modular operad". In the last part of the paper we define a reduced version of stated skein algebras and prove that it allows to recover Bonahon-Wong's quantum trace map and interpret skein algebras in the classical limit when $q\to 1$ as regular functions over a suitable version of moduli spaces of twisted bundles. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1907.11400v2-abstract-full').style.display = 'none'; document.getElementById('1907.11400v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 November, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 26 July, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">74 pages, 33 figures. In version 2 : strengthened Theorem 4.17. To be published in the Journal of the European Mathematical Society</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> Primary 57N10; secondary 57M25 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1812.11628">arXiv:1812.11628</a> <span> [<a href="https://arxiv.org/pdf/1812.11628">pdf</a>, <a href="https://arxiv.org/format/1812.11628">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Mathematical Physics">math-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.2140/agt.2023.23.339">10.2140/agt.2023.23.339 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> ${\rm SL}_2$ quantum trace in quantum Teichm眉ller theory via writhe </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Kim%2C+H+K">Hyun Kyu Kim</a>, <a href="/search/?searchtype=author&query=L%C3%AA%2C+T+T+Q">Thang T. Q. L锚</a>, <a href="/search/?searchtype=author&query=Son%2C+M">Miri Son</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1812.11628v3-abstract-short" style="display: inline;"> Quantization of the Teichm眉ller space of a punctured Riemann surface $S$ is an approach to $3$-dimensional quantum gravity, and is a prototypical example of quantization of cluster varieties. Any simple loop $纬$ in $S$ gives rise to a natural trace-of-monodromy function $\mathbb{I}(纬)$ on the Teichm眉ller space. For any ideal triangulation $螖$ of $S$, this function $\mathbb{I}(纬)$ is a Laurent poly… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1812.11628v3-abstract-full').style.display = 'inline'; document.getElementById('1812.11628v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1812.11628v3-abstract-full" style="display: none;"> Quantization of the Teichm眉ller space of a punctured Riemann surface $S$ is an approach to $3$-dimensional quantum gravity, and is a prototypical example of quantization of cluster varieties. Any simple loop $纬$ in $S$ gives rise to a natural trace-of-monodromy function $\mathbb{I}(纬)$ on the Teichm眉ller space. For any ideal triangulation $螖$ of $S$, this function $\mathbb{I}(纬)$ is a Laurent polynomial in the square-roots of the exponentiated shear coordinates for the arcs of $螖$. An important problem was to construct a quantization of this function $\mathbb{I}(纬)$, namely to replace it by a noncommutative Laurent polynomial in the quantum variables. This problem, which is closely related to the framed protected spin characters in physics, has been solved by Allegretti and Kim using Bonahon and Wong's ${\rm SL}_2$ quantum trace for skein algebras, and by Gabella using Gaiotto, Moore and Neitzke's Seiberg-Witten curves, spectral networks, and writhe of links. We show that these two solutions to the quantization problem coincide. We enhance Gabella's solution and show that it is a twist of the Bonahon-Wong quantum trace. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1812.11628v3-abstract-full').style.display = 'none'; document.getElementById('1812.11628v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 31 March, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 30 December, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">45 pages. ver2: Author added. Sections 4, 5, statement and proof of main theorem substantially improved / ver3: Changes made for published version have been reflected</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 53D55; 81R60; 51P05; 46L65; 46L85; 13F60 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Algebr. Geom. Topol. 23 (2023) 339-418 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1804.09303">arXiv:1804.09303</a> <span> [<a href="https://arxiv.org/pdf/1804.09303">pdf</a>, <a href="https://arxiv.org/ps/1804.09303">ps</a>, <a href="https://arxiv.org/format/1804.09303">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.2140/agt.2019.19.3453">10.2140/agt.2019.19.3453 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> On Kauffman bracket skein modules of marked 3-manifolds and the Chebyshev-Frobenius homomorphism </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Le%2C+T+T+Q">Thang T. Q. Le</a>, <a href="/search/?searchtype=author&query=Paprocki%2C+J">Jonathan Paprocki</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1804.09303v2-abstract-short" style="display: inline;"> In this paper we study the skein algebras of marked surfaces and the skein modules of marked 3-manifolds. Muller showed that skein algebras of totally marked surfaces may be embedded in easy to study algebras known as quantum tori. We first extend Muller's result to permit marked surfaces with unmarked boundary components. The addition of unmarked components allows us to develop a surgery theory w… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1804.09303v2-abstract-full').style.display = 'inline'; document.getElementById('1804.09303v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1804.09303v2-abstract-full" style="display: none;"> In this paper we study the skein algebras of marked surfaces and the skein modules of marked 3-manifolds. Muller showed that skein algebras of totally marked surfaces may be embedded in easy to study algebras known as quantum tori. We first extend Muller's result to permit marked surfaces with unmarked boundary components. The addition of unmarked components allows us to develop a surgery theory which enables us to extend the Chebyshev homomorphism of Bonahon and Wong between skein algebras of unmarked surfaces to a "Chebyshev-Frobenius homomorphism" between skein modules of marked 3-manifolds. We show that the image of the Chebyshev-Frobenius homomorphism is either transparent or skew-transparent. In addition, we make use of the Muller algebra method to calculate the center of the skein algebra of a marked surface when the quantum parameter is not a root of unity. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1804.09303v2-abstract-full').style.display = 'none'; document.getElementById('1804.09303v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 November, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 24 April, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">39 pages, 19 figures. Fixed typos, two new figures, cosmetic changes, clarified definition of trivial arc relation element</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57N10; 57M25 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Algebr. Geom. Topol. 19 (2019) 3453-3509 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1802.00705">arXiv:1802.00705</a> <span> [<a href="https://arxiv.org/pdf/1802.00705">pdf</a>, <a href="https://arxiv.org/format/1802.00705">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Materials Science">cond-mat.mtrl-sci</span> </div> </div> <p class="title is-5 mathjax"> Tuning the magnetodynamic properties of all-perpendicular spin valves using He+ irradiation </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Jiang%2C+S">S. Jiang</a>, <a href="/search/?searchtype=author&query=Chung%2C+S">S. Chung</a>, <a href="/search/?searchtype=author&query=Diez%2C+L+H">L. Herrera Diez</a>, <a href="/search/?searchtype=author&query=Le%2C+T+Q">T. Q. Le</a>, <a href="/search/?searchtype=author&query=Magnusson%2C+F">F. Magnusson</a>, <a href="/search/?searchtype=author&query=Ravelosona%2C+D">D. Ravelosona</a>, <a href="/search/?searchtype=author&query=%C3%85kerman%2C+J">J. 脜kerman</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1802.00705v1-abstract-short" style="display: inline;"> Using He+ ion irradiation, we demonstrate how the magnetodynamic properties of both ferromagnetic layers in all-perpendicular [Co/Pd]/Cu/[Co/Ni] spin valves can be tuned by varying the He+ ion fluence. As the perpendicular magnetic anisotropy of both layers is gradually reduced by the irradiation, different magnetic configurations can be achieved from all-perpendicular, through orthogonal, to all… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1802.00705v1-abstract-full').style.display = 'inline'; document.getElementById('1802.00705v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1802.00705v1-abstract-full" style="display: none;"> Using He+ ion irradiation, we demonstrate how the magnetodynamic properties of both ferromagnetic layers in all-perpendicular [Co/Pd]/Cu/[Co/Ni] spin valves can be tuned by varying the He+ ion fluence. As the perpendicular magnetic anisotropy of both layers is gradually reduced by the irradiation, different magnetic configurations can be achieved from all-perpendicular, through orthogonal, to all in-plane. In addition, both the magnetic damping and the inhomogeneous broadening of the Co/Ni layer improve substantially with increasing fluence. GMR of the spin valve is negatively affected and decreases linearly from an original value of 1.14% to 0.4% at the maximum fluence of 50*10^14 He+/cm^2. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1802.00705v1-abstract-full').style.display = 'none'; document.getElementById('1802.00705v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 February, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">5 Pages, 4 Figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1609.04987">arXiv:1609.04987</a> <span> [<a href="https://arxiv.org/pdf/1609.04987">pdf</a>, <a href="https://arxiv.org/ps/1609.04987">ps</a>, <a href="https://arxiv.org/format/1609.04987">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> </div> <p class="title is-5 mathjax"> Triangular decomposition of skein algebras </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Le%2C+T+T+Q">Thang T. Q. Le</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1609.04987v1-abstract-short" style="display: inline;"> By introducing a finer version of the Kauffman bracket skein algebra, we show how to decompose the Kauffman bracket skein algebra of a surface into elementary blocks corresponding to the triangles in an ideal triangulation of the surface. The new skein algebra of an ideal triangle has a simple presentation. This gives an easy proof of the existence of the quantum trace map of Bonahon and Wong. We… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1609.04987v1-abstract-full').style.display = 'inline'; document.getElementById('1609.04987v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1609.04987v1-abstract-full" style="display: none;"> By introducing a finer version of the Kauffman bracket skein algebra, we show how to decompose the Kauffman bracket skein algebra of a surface into elementary blocks corresponding to the triangles in an ideal triangulation of the surface. The new skein algebra of an ideal triangle has a simple presentation. This gives an easy proof of the existence of the quantum trace map of Bonahon and Wong. We also explain the relation between our skein algebra and the one defined by Muller, and use it to show that the quantum trace map can be extended to the Muller skein algebra. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1609.04987v1-abstract-full').style.display = 'none'; document.getElementById('1609.04987v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 September, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">30 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57N10; 57M25 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1604.08502">arXiv:1604.08502</a> <span> [<a href="https://arxiv.org/pdf/1604.08502">pdf</a>, <a href="https://arxiv.org/format/1604.08502">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1215/00127094-2017-0030">10.1215/00127094-2017-0030 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The colored HOMFLYPT function is $q$-holonomic </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Garoufalidis%2C+S">Stavros Garoufalidis</a>, <a href="/search/?searchtype=author&query=Lauda%2C+A+D">Aaron D. Lauda</a>, <a href="/search/?searchtype=author&query=L%C3%AA%2C+T+T+Q">Thang T. Q. L锚</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1604.08502v2-abstract-short" style="display: inline;"> We prove that the HOMFLYPT polynomial of a link, colored by partitions with a fixed number of rows is a $q$-holonomic function. Specializing to the case of knots colored by a partition with a single row, it proves the existence of an $(a,q)$ super-polynomial of knots in 3-space, as was conjectured by string theorists. Our proof uses skew Howe duality that reduces the evaluation of web diagrams and… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1604.08502v2-abstract-full').style.display = 'inline'; document.getElementById('1604.08502v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1604.08502v2-abstract-full" style="display: none;"> We prove that the HOMFLYPT polynomial of a link, colored by partitions with a fixed number of rows is a $q$-holonomic function. Specializing to the case of knots colored by a partition with a single row, it proves the existence of an $(a,q)$ super-polynomial of knots in 3-space, as was conjectured by string theorists. Our proof uses skew Howe duality that reduces the evaluation of web diagrams and their ladders to a Poincare-Birkhoff-Witt computation of an auxiliary quantum group of rank the number of strings of the ladder diagram. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1604.08502v2-abstract-full').style.display = 'none'; document.getElementById('1604.08502v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 February, 2017; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 28 April, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">38 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Duke Math. J. 167, no. 3 (2018), 397-447 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1603.08265">arXiv:1603.08265</a> <span> [<a href="https://arxiv.org/pdf/1603.08265">pdf</a>, <a href="https://arxiv.org/ps/1603.08265">ps</a>, <a href="https://arxiv.org/format/1603.08265">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> </div> </div> <p class="title is-5 mathjax"> On positivity of Kauffman bracket skein algebras of surfaces </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=L%C3%AA%2C+T+T+Q">Thang T. Q. L锚</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1603.08265v2-abstract-short" style="display: inline;"> We show that the Chebyshev polynomials form a basic block of any positive basis of the Kauffman bracket skein algebras of surfaces. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1603.08265v2-abstract-full" style="display: none;"> We show that the Chebyshev polynomials form a basic block of any positive basis of the Kauffman bracket skein algebras of surfaces. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1603.08265v2-abstract-full').style.display = 'none'; document.getElementById('1603.08265v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 October, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 27 March, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">11 pages. Typos corrected. Details added. Theorem 3.2 is strengthened. To appear in IMRN</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57M27; 57M25 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1601.07487">arXiv:1601.07487</a> <span> [<a href="https://arxiv.org/pdf/1601.07487">pdf</a>, <a href="https://arxiv.org/format/1601.07487">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Combinatorics">math.CO</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> </div> <p class="title is-5 mathjax"> A survey of $q$-holonomic functions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Garoufalidis%2C+S">Stavros Garoufalidis</a>, <a href="/search/?searchtype=author&query=Le%2C+T+T+Q">T. T. Q. Le</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1601.07487v2-abstract-short" style="display: inline;"> We give a survey of basic facts of $q$-holonomic functions of one or several variables, following Zeilberger and Sabbah. We provide detailed proofs and examples. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1601.07487v2-abstract-full" style="display: none;"> We give a survey of basic facts of $q$-holonomic functions of one or several variables, following Zeilberger and Sabbah. We provide detailed proofs and examples. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1601.07487v2-abstract-full').style.display = 'none'; document.getElementById('1601.07487v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 September, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 27 January, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">21 pages, latex</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1511.06054">arXiv:1511.06054</a> <span> [<a href="https://arxiv.org/pdf/1511.06054">pdf</a>, <a href="https://arxiv.org/ps/1511.06054">ps</a>, <a href="https://arxiv.org/format/1511.06054">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1017/S1474748017000068">10.1017/S1474748017000068 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Quantum Teichm眉ller spaces and quantum trace map </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=L%C3%AA%2C+T+T+Q">Thang T. Q. L锚</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1511.06054v4-abstract-short" style="display: inline;"> We show how the quantum trace map of Bonahon and Wong can be constructed in a natural way using the skein algebra of Muller, which is an extension of the Kauffman bracket skein algebra of surfaces. We also show that the quantum Teichm眉ller space of a marked surface, defined by Chekhov-Fock (and Kashaev) in an abstract way, can be realized as a concrete subalgebra of the skew field of the skein alg… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1511.06054v4-abstract-full').style.display = 'inline'; document.getElementById('1511.06054v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1511.06054v4-abstract-full" style="display: none;"> We show how the quantum trace map of Bonahon and Wong can be constructed in a natural way using the skein algebra of Muller, which is an extension of the Kauffman bracket skein algebra of surfaces. We also show that the quantum Teichm眉ller space of a marked surface, defined by Chekhov-Fock (and Kashaev) in an abstract way, can be realized as a concrete subalgebra of the skew field of the skein algebra. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1511.06054v4-abstract-full').style.display = 'none'; document.getElementById('1511.06054v4-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 October, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 18 November, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Final version. To appear in Journal of the Institute of Mathematics of Jussieu</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57M25; 57M27 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> J. Inst. Math. Jussieu 18 (2019) 249-291 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1509.03277">arXiv:1509.03277</a> <span> [<a href="https://arxiv.org/pdf/1509.03277">pdf</a>, <a href="https://arxiv.org/ps/1509.03277">ps</a>, <a href="https://arxiv.org/format/1509.03277">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.2140/agt.2017.17.157">10.2140/agt.2017.17.157 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Character varieties, A-polynomials, and the AJ Conjecture </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Le%2C+T+T+Q">Thang T. Q. Le</a>, <a href="/search/?searchtype=author&query=Zhang%2C+X">Xingru Zhang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1509.03277v1-abstract-short" style="display: inline;"> We establish some facts about the behavior of the rational-geometric subvariety of the $SL_2(\c)$ or $PSL_2(\c)$ character variety of a hyperbolic knot manifold under the restriction map to the $SL_2(\c)$ or $PSL_2(\c)$ character variety of the boundary torus, and use the results to get some properties about the A-polynomials and to prove the AJ conjecture for certain class of knots in $S^3$ inclu… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1509.03277v1-abstract-full').style.display = 'inline'; document.getElementById('1509.03277v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1509.03277v1-abstract-full" style="display: none;"> We establish some facts about the behavior of the rational-geometric subvariety of the $SL_2(\c)$ or $PSL_2(\c)$ character variety of a hyperbolic knot manifold under the restriction map to the $SL_2(\c)$ or $PSL_2(\c)$ character variety of the boundary torus, and use the results to get some properties about the A-polynomials and to prove the AJ conjecture for certain class of knots in $S^3$ including in particular any $2$-bridge knot over which the double branched cover of $S^3$ is a lens space of prime order. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1509.03277v1-abstract-full').style.display = 'none'; document.getElementById('1509.03277v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 September, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">24 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Algebr. Geom. Topol. 17 (2017) 157-188 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1503.03549">arXiv:1503.03549</a> <span> [<a href="https://arxiv.org/pdf/1503.03549">pdf</a>, <a href="https://arxiv.org/ps/1503.03549">ps</a>, <a href="https://arxiv.org/format/1503.03549">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.2140/gt.2016.20.2687">10.2140/gt.2016.20.2687 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Unified quantum invariants for integral homology spheres associated with simple Lie algebras </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Habiro%2C+K">Kazuo Habiro</a>, <a href="/search/?searchtype=author&query=L%C3%AA%2C+T+T+Q">Thang T. Q. L锚</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1503.03549v2-abstract-short" style="display: inline;"> For each finite dimensional, simple, complex Lie algebra $\mathfrak g$ and each root of unity $尉$ (with some mild restriction on the order) one can define the Witten-Reshetikhin-Turaev (WRT) quantum invariant $蟿_M^{\mathfrak g}(尉)\in \mathbb C$ of oriented 3-manifolds $M$. In the present paper we construct an invariant $J_M$ of integral homology spheres $M$ with values in the cyclotomic completion… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1503.03549v2-abstract-full').style.display = 'inline'; document.getElementById('1503.03549v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1503.03549v2-abstract-full" style="display: none;"> For each finite dimensional, simple, complex Lie algebra $\mathfrak g$ and each root of unity $尉$ (with some mild restriction on the order) one can define the Witten-Reshetikhin-Turaev (WRT) quantum invariant $蟿_M^{\mathfrak g}(尉)\in \mathbb C$ of oriented 3-manifolds $M$. In the present paper we construct an invariant $J_M$ of integral homology spheres $M$ with values in the cyclotomic completion $\widehat {\mathbb Z [q]}$ of the polynomial ring $\mathbb Z [q]$, such that the evaluation of $J_M$ at each root of unity gives the WRT quantum invariant of $M$ at that root of unity. This result generalizes the case ${\mathfrak g}=sl_2$ proved by the first author. It follows that $J_M$ unifies all the quantum invariants of $M$ associated with $\mathfrak g$, and represents the quantum invariants as a kind of "analytic function" defined on the set of roots of unity. For example, $蟿_M(尉)$ for all roots of unity are determined by a "Taylor expansion" at any root of unity, and also by the values at infinitely many roots of unity of prime power orders. It follows that WRT quantum invariants $蟿_M(尉)$ for all roots of unity are determined by the Ohtsuki series, which can be regarded as the Taylor expansion at $q=1$, and hence by the Le-Murakami-Ohtsuki invariant. Another consequence is that the WRT quantum invariants $蟿_M^{ \mathfrak g}(尉)$ are algebraic integers. The construction of the invariant $J_M$ is done on the level of quantum group, and does not involve any finite dimensional representation, unlike the definition of the WRT quantum invariant. Thus, our construction gives a unified, "representation-free" definition of the quantum invariants of integral homology spheres. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1503.03549v2-abstract-full').style.display = 'none'; document.getElementById('1503.03549v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 November, 2015; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 11 March, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">125 pages. Accepted for publication in "Geometry and Topology"</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57M27; 17B37 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Geom. Topol. 20 (2016) 2687-2835 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1312.3705">arXiv:1312.3705</a> <span> [<a href="https://arxiv.org/pdf/1312.3705">pdf</a>, <a href="https://arxiv.org/ps/1312.3705">ps</a>, <a href="https://arxiv.org/format/1312.3705">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.2140/agt.2015.15.1093">10.2140/agt.2015.15.1093 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> On Kauffman Bracket Skein Modules at Root of Unity </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Le%2C+T+T+Q">Thang T. Q. Le</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1312.3705v2-abstract-short" style="display: inline;"> We reprove and expand results of Bonahon and Wong on central elements of the Kauffman bracket skein modules at root of 1 and on the existence of the Chebyshev homomorphism, using elementary skein methods. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1312.3705v2-abstract-full" style="display: none;"> We reprove and expand results of Bonahon and Wong on central elements of the Kauffman bracket skein modules at root of 1 and on the existence of the Chebyshev homomorphism, using elementary skein methods. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1312.3705v2-abstract-full').style.display = 'none'; document.getElementById('1312.3705v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 September, 2014; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 13 December, 2013; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2013. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Minor revision. Typos fixed. To appear in Algebraic and Geometric Topology</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Algebr. Geom. Topol. 15 (2015) 1093-1117 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1212.6777">arXiv:1212.6777</a> <span> [<a href="https://arxiv.org/pdf/1212.6777">pdf</a>, <a href="https://arxiv.org/ps/1212.6777">ps</a>, <a href="https://arxiv.org/format/1212.6777">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Algebraic Topology">math.AT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.2140/agt.2013.13.2383">10.2140/agt.2013.13.2383 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Growth of regulators in finite abelian coverings </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Le%2C+T+T+Q">Thang T. Q. Le</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1212.6777v1-abstract-short" style="display: inline;"> We show that the regulator, which is the difference between the homology torsion and the combinatorial Ray-Singer torsion, of fnite abelian coverings of a fixed complex has sub-exponential growth rate. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1212.6777v1-abstract-full" style="display: none;"> We show that the regulator, which is the difference between the homology torsion and the combinatorial Ray-Singer torsion, of fnite abelian coverings of a fixed complex has sub-exponential growth rate. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1212.6777v1-abstract-full').style.display = 'none'; document.getElementById('1212.6777v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 December, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2012. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">13 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 54H20; 56S30; 57Q10; 37B50; 37B10; 43A07 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Algebr. Geom. Topol. 13 (2013) 2383-2404 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1112.3905">arXiv:1112.3905</a> <span> [<a href="https://arxiv.org/pdf/1112.3905">pdf</a>, <a href="https://arxiv.org/ps/1112.3905">ps</a>, <a href="https://arxiv.org/format/1112.3905">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> </div> </div> <p class="title is-5 mathjax"> Nahm sums, stability and the colored Jones polynomial </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Garoufalidis%2C+S">Stavros Garoufalidis</a>, <a href="/search/?searchtype=author&query=Le%2C+T+T+Q">Thang T. Q. Le</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1112.3905v2-abstract-short" style="display: inline;"> Nahm sums are $q$-series of a special hypergeometric type that appear in character formulas in Conformal Field Theory, and give rise to elements of the Bloch group, and have interesting modularity properties. In our paper, we show how Nahm sums arise naturally in Quantum Knot Theory, namely we prove the stability of the coefficients of the colored Jones polynomial of an alternating link and presen… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1112.3905v2-abstract-full').style.display = 'inline'; document.getElementById('1112.3905v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1112.3905v2-abstract-full" style="display: none;"> Nahm sums are $q$-series of a special hypergeometric type that appear in character formulas in Conformal Field Theory, and give rise to elements of the Bloch group, and have interesting modularity properties. In our paper, we show how Nahm sums arise naturally in Quantum Knot Theory, namely we prove the stability of the coefficients of the colored Jones polynomial of an alternating link and present a Nahm sum formula for the resulting power series, defined in terms of a reduced diagram of the alternating link. The Nahm sum formula comes with a computer implementation, illustrated in numerous examples of proven or conjectural identities among $q$-series. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1112.3905v2-abstract-full').style.display = 'none'; document.getElementById('1112.3905v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 May, 2012; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 16 December, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2011. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Latex, 57 pages and 111 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1111.5258">arXiv:1111.5258</a> <span> [<a href="https://arxiv.org/pdf/1111.5258">pdf</a>, <a href="https://arxiv.org/ps/1111.5258">ps</a>, <a href="https://arxiv.org/format/1111.5258">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> </div> <p class="title is-5 mathjax"> On the AJ conjecture for knots </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Le%2C+T+T+Q">Thang T. Q. Le</a>, <a href="/search/?searchtype=author&query=Tran%2C+A+T">Anh T. Tran</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1111.5258v4-abstract-short" style="display: inline;"> We confirm the AJ conjecture [Ga04] that relates the A-polynomial and the colored Jones polynomial for those hyperbolic knots satisfying certain conditions. In particular, we show that the conjecture holds true for some classes of two-bridge knots and pretzel knots. This extends the result of the first author in [Le06] where he established the AJ conjecture for a large class of two-bridge knots, i… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1111.5258v4-abstract-full').style.display = 'inline'; document.getElementById('1111.5258v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1111.5258v4-abstract-full" style="display: none;"> We confirm the AJ conjecture [Ga04] that relates the A-polynomial and the colored Jones polynomial for those hyperbolic knots satisfying certain conditions. In particular, we show that the conjecture holds true for some classes of two-bridge knots and pretzel knots. This extends the result of the first author in [Le06] where he established the AJ conjecture for a large class of two-bridge knots, including all twist knots. Along the way, we explicitly calculate the universal character ring of the knot group of the (-2,3,2n+1)-pretzel knot and show that it is reduced for all integers n. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1111.5258v4-abstract-full').style.display = 'none'; document.getElementById('1111.5258v4-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 January, 2014; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 November, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2011. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57N10 (Primary) 57M25 (Secondary) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1111.0332">arXiv:1111.0332</a> <span> [<a href="https://arxiv.org/pdf/1111.0332">pdf</a>, <a href="https://arxiv.org/ps/1111.0332">ps</a>, <a href="https://arxiv.org/format/1111.0332">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> </div> <p class="title is-5 mathjax"> The Kauffman bracket skein module of two-bridge links </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Le%2C+T+T+Q">Thang T. Q. Le</a>, <a href="/search/?searchtype=author&query=Tran%2C+A+T">Anh T. Tran</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1111.0332v2-abstract-short" style="display: inline;"> We calculate the Kauffman bracket skein module (KBSM) of the complement of all two-bridge links. For a two-bridge link, we show that the KBSM of its complement is free over the ring $\BC[t^{\pm 1}]$ and when reducing $t=-1$, it is isomorphic to the ring of regular functions on the character variety of the link group. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1111.0332v2-abstract-full" style="display: none;"> We calculate the Kauffman bracket skein module (KBSM) of the complement of all two-bridge links. For a two-bridge link, we show that the KBSM of its complement is free over the ring $\BC[t^{\pm 1}]$ and when reducing $t=-1$, it is isomorphic to the ring of regular functions on the character variety of the link group. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1111.0332v2-abstract-full').style.display = 'none'; document.getElementById('1111.0332v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 September, 2012; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 1 November, 2011; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2011. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Very minor changes. To appear in the Proceedings of the AMS</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57N10 (Primary) 57M25 (Secondary) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1005.3895">arXiv:1005.3895</a> <span> [<a href="https://arxiv.org/pdf/1005.3895">pdf</a>, <a href="https://arxiv.org/ps/1005.3895">ps</a>, <a href="https://arxiv.org/format/1005.3895">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1112/jtopol/jts010">10.1112/jtopol/jts010 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The perturbative invariants of rational homology 3-spheres can be recovered from the LMO invariant </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Kuriya%2C+T">Takahito Kuriya</a>, <a href="/search/?searchtype=author&query=Le%2C+T+T+Q">Thang T. Q. Le</a>, <a href="/search/?searchtype=author&query=Ohtsuki%2C+T">Tomotada Ohtsuki</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1005.3895v1-abstract-short" style="display: inline;"> We show that the perturbative ${\frak g}$ invariant of rational homology 3-spheres can be recovered from the LMO invariant for any simple Lie algebra ${\frak g}$, i.e, the LMO invariant is universal among the perturbative invariants. This universality was conjectured in [25]. Since the perturbative invariants dominate the quantum invariants of integral homology 3-spheres [13,14,15], this implies t… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1005.3895v1-abstract-full').style.display = 'inline'; document.getElementById('1005.3895v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1005.3895v1-abstract-full" style="display: none;"> We show that the perturbative ${\frak g}$ invariant of rational homology 3-spheres can be recovered from the LMO invariant for any simple Lie algebra ${\frak g}$, i.e, the LMO invariant is universal among the perturbative invariants. This universality was conjectured in [25]. Since the perturbative invariants dominate the quantum invariants of integral homology 3-spheres [13,14,15], this implies that the LMO invariant dominates the quantum invariants of integral homology 3-spheres. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1005.3895v1-abstract-full').style.display = 'none'; document.getElementById('1005.3895v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 May, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2010. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">30 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57M27 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0907.0172">arXiv:0907.0172</a> <span> [<a href="https://arxiv.org/pdf/0907.0172">pdf</a>, <a href="https://arxiv.org/ps/0907.0172">ps</a>, <a href="https://arxiv.org/format/0907.0172">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> </div> <p class="title is-5 mathjax"> On the Volume Conjecture for Cables of Knots </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Le%2C+T+T+Q">Thang T. Q. Le</a>, <a href="/search/?searchtype=author&query=Tran%2C+A+T">Anh T. Tran</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0907.0172v3-abstract-short" style="display: inline;"> We establish the volume conjecture for (m,2)-cables of the figure 8 knot, when m is odd. For (m,2)-cables of general knots where m is even, we show that the limit in the volume conjecture depends on the parity of the color (of the Kashaev invariant). There are many cases when the volume conjecture for cables of the figure 8 knot is false if one considers all the colors, but holds true if one res… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0907.0172v3-abstract-full').style.display = 'inline'; document.getElementById('0907.0172v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0907.0172v3-abstract-full" style="display: none;"> We establish the volume conjecture for (m,2)-cables of the figure 8 knot, when m is odd. For (m,2)-cables of general knots where m is even, we show that the limit in the volume conjecture depends on the parity of the color (of the Kashaev invariant). There are many cases when the volume conjecture for cables of the figure 8 knot is false if one considers all the colors, but holds true if one restricts the colors to a subset of the set of positive integers. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0907.0172v3-abstract-full').style.display = 'none'; document.getElementById('0907.0172v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 August, 2009; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 1 July, 2009; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2009. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Corrected proof of Lemma 4.5. Accepted to publish in JKTR</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57N10; 57M25 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0809.2572">arXiv:0809.2572</a> <span> [<a href="https://arxiv.org/pdf/0809.2572">pdf</a>, <a href="https://arxiv.org/ps/0809.2572">ps</a>, <a href="https://arxiv.org/format/0809.2572">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.3842/SIGMA.2008.080">10.3842/SIGMA.2008.080 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Analyticity of the Free Energy of a Closed 3-Manifold </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Garoufalidis%2C+S">Stavros Garoufalidis</a>, <a href="/search/?searchtype=author&query=Le%2C+T+T+Q">Thang T. Q. Le</a>, <a href="/search/?searchtype=author&query=Marino%2C+M">Marcos Marino</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0809.2572v5-abstract-short" style="display: inline;"> The free energy of a closed 3-manifold is a 2-parameter formal power series which encodes the perturbative Chern-Simons invariant (also known as the LMO invariant) of a closed 3-manifold with gauge group U(N) for arbitrary $N$. We prove that the free energy of an arbitrary closed 3-manifold is uniformly Gevrey-1. As a corollary, it follows that the genus $g$ part of the free energy is convergent… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0809.2572v5-abstract-full').style.display = 'inline'; document.getElementById('0809.2572v5-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0809.2572v5-abstract-full" style="display: none;"> The free energy of a closed 3-manifold is a 2-parameter formal power series which encodes the perturbative Chern-Simons invariant (also known as the LMO invariant) of a closed 3-manifold with gauge group U(N) for arbitrary $N$. We prove that the free energy of an arbitrary closed 3-manifold is uniformly Gevrey-1. As a corollary, it follows that the genus $g$ part of the free energy is convergent in a neighborhood of zero, independent of the genus. Our results follow from an estimate of the LMO invariant, in a particular gauge, and from recent results of Bender-Gao-Richmond on the asymptotics of the number of rooted maps for arbitrary genus. We illustrate our results with an explicit formula for the free energy of a Lens space. In addition, using the Painlev茅 differential equation, we obtain an asymptotic expansion for the number of cubic graphs to all orders, stengthening the results of Bender-Gao-Richmond. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0809.2572v5-abstract-full').style.display = 'none'; document.getElementById('0809.2572v5-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 November, 2008; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 15 September, 2008; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2008. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">This is a contribution to the Special Issue on Deformation Quantization, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57M27 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> SIGMA 4 (2008), 080, 20 pages </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0706.2017">arXiv:0706.2017</a> <span> [<a href="https://arxiv.org/pdf/0706.2017">pdf</a>, <a href="https://arxiv.org/ps/0706.2017">ps</a>, <a href="https://arxiv.org/format/0706.2017">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> </div> </div> <p class="title is-5 mathjax"> Twisted Alexander polynomial of links in the projective space </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Huynh%2C+V+Q">Vu Q. Huynh</a>, <a href="/search/?searchtype=author&query=Le%2C+T+T+Q">Thang T. Q. Le</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0706.2017v1-abstract-short" style="display: inline;"> We use Reidemeister torsion to study a twisted Alexander polynomial, as defined by Turaev, for links in the projective space. Using sign-refined torsion we derive a skein relation for a normalized form of this polynomial. </span> <span class="abstract-full has-text-grey-dark mathjax" id="0706.2017v1-abstract-full" style="display: none;"> We use Reidemeister torsion to study a twisted Alexander polynomial, as defined by Turaev, for links in the projective space. Using sign-refined torsion we derive a skein relation for a normalized form of this polynomial. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0706.2017v1-abstract-full').style.display = 'none'; document.getElementById('0706.2017v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 June, 2007; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2007. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">To appear on Journal of Knot Theory and Its Ramifications</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57M25; 57M05 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0704.3669">arXiv:0704.3669</a> <span> [<a href="https://arxiv.org/pdf/0704.3669">pdf</a>, <a href="https://arxiv.org/ps/0704.3669">ps</a>, <a href="https://arxiv.org/format/0704.3669">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> </div> </div> <p class="title is-5 mathjax"> Unified quantum invariants and their refinements for homology 3-spheres with 2-torsion </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Beliakova%2C+A">Anna Beliakova</a>, <a href="/search/?searchtype=author&query=Blanchet%2C+C">Christian Blanchet</a>, <a href="/search/?searchtype=author&query=Le%2C+T+T+Q">Thang T. Q. Le</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="0704.3669v1-abstract-short" style="display: inline;"> For every rational homology 3-sphere with 2-torsion only we construct a unified invariant (which takes values in a certain cyclotomic completion of a polynomial ring), such that the evaluation of this invariant at any odd root of unity provides the SO(3) Witten-Reshetikhin-Turaev invariant at this root and at any even root of unity the SU(2) quantum invariant. Moreover, this unified invariant sp… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0704.3669v1-abstract-full').style.display = 'inline'; document.getElementById('0704.3669v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0704.3669v1-abstract-full" style="display: none;"> For every rational homology 3-sphere with 2-torsion only we construct a unified invariant (which takes values in a certain cyclotomic completion of a polynomial ring), such that the evaluation of this invariant at any odd root of unity provides the SO(3) Witten-Reshetikhin-Turaev invariant at this root and at any even root of unity the SU(2) quantum invariant. Moreover, this unified invariant splits into a sum of the refined unified invariants dominating spin and cohomological refinements of quantum SU(2) invariants. New results on the Ohtsuki series and the integrality of quantum invariants are the main applications of our construction. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0704.3669v1-abstract-full').style.display = 'none'; document.getElementById('0704.3669v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 April, 2007; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2007. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">23 pages, results of math.QA/0510382 are included</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57N10; 57M25 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Fund. math., 201 (2008), pp. 217-239 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/math/0609618">arXiv:math/0609618</a> <span> [<a href="https://arxiv.org/pdf/math/0609618">pdf</a>, <a href="https://arxiv.org/ps/math/0609618">ps</a>, <a href="https://arxiv.org/format/math/0609618">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> </div> </div> <p class="title is-5 mathjax"> Gevrey series in quantum topology </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Garoufalidis%2C+S">Stavros Garoufalidis</a>, <a href="/search/?searchtype=author&query=Le%2C+T+T+Q">T. T. Q. Le</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="math/0609618v2-abstract-short" style="display: inline;"> Our aim is to prove that two formal power series of importance to quantum topology are Gevrey. These series are the Kashaev invariant of a knot (reformulated by Huynh and the second author) and the Gromov norm of the LMO of an integral homology 3-sphere. It follows that the power series associated to a simple Lie algebra and a homology sphere is Gevrey. Contrary to the case of analysis, our form… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0609618v2-abstract-full').style.display = 'inline'; document.getElementById('math/0609618v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="math/0609618v2-abstract-full" style="display: none;"> Our aim is to prove that two formal power series of importance to quantum topology are Gevrey. These series are the Kashaev invariant of a knot (reformulated by Huynh and the second author) and the Gromov norm of the LMO of an integral homology 3-sphere. It follows that the power series associated to a simple Lie algebra and a homology sphere is Gevrey. Contrary to the case of analysis, our formal power series are not solutions to differential equations with polynomial coefficients. The first author has conjectured (and in some cases proved, in joint work with Costin) that our formal power series have resurgent Borel transform, with geometrically interesting set of singularities. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0609618v2-abstract-full').style.display = 'none'; document.getElementById('math/0609618v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 February, 2007; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 21 September, 2006; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2006. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">19 pages, 8 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57N10 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/math/0608627">arXiv:math/0608627</a> <span> [<a href="https://arxiv.org/pdf/math/0608627">pdf</a>, <a href="https://arxiv.org/ps/math/0608627">ps</a>, <a href="https://arxiv.org/format/math/0608627">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> </div> <p class="title is-5 mathjax"> Integrality of quantum 3-manifold invariants and rational surgery formula </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Beliakova%2C+A">Anna Beliakova</a>, <a href="/search/?searchtype=author&query=Le%2C+T+T+Q">Thang T. Q. Le</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="math/0608627v2-abstract-short" style="display: inline;"> We prove that the Witten-Reshetikhin-Turaev (WRT) SO(3) invariant of an arbitrary 3-manifold M is always an algebraic integer. Moreover, we give a rational surgery formula for the unified invariant dominating WRT SO(3) invariants of rational homology 3-spheres at roots of unity of order co-prime with the torsion. As an application, we compute the unified invariant for Seifert fibered spaces and… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0608627v2-abstract-full').style.display = 'inline'; document.getElementById('math/0608627v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="math/0608627v2-abstract-full" style="display: none;"> We prove that the Witten-Reshetikhin-Turaev (WRT) SO(3) invariant of an arbitrary 3-manifold M is always an algebraic integer. Moreover, we give a rational surgery formula for the unified invariant dominating WRT SO(3) invariants of rational homology 3-spheres at roots of unity of order co-prime with the torsion. As an application, we compute the unified invariant for Seifert fibered spaces and for Dehn surgeries on twist knots. We show that this invariant separates integral homology Seifert fibered spaces and can be used to detect the unknot. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0608627v2-abstract-full').style.display = 'none'; document.getElementById('math/0608627v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 April, 2007; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 25 August, 2006; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2006. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">18 pages, Compositio Math. in press</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57N10; 57M25 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Compositio Mathematica, vol. 143, Issue 06 (2007), 1593-1612 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/math/0602097">arXiv:math/0602097</a> <span> [<a href="https://arxiv.org/pdf/math/0602097">pdf</a>, <a href="https://arxiv.org/ps/math/0602097">ps</a>, <a href="https://arxiv.org/format/math/0602097">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> </div> </div> <p class="title is-5 mathjax"> 3-cobordisms with their rational homology on the boundary </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Cheptea%2C+D">Dorin Cheptea</a>, <a href="/search/?searchtype=author&query=Le%2C+T+T+Q">Thang T Q Le</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="math/0602097v1-abstract-short" style="display: inline;"> The object of this paper is to define a subcategory of the category of 3-cobordisms to which invariants of rational homology 3-spheres should generalize. We specify the notion of Topological Quantum Field Theory (in the sense of Atiyah) to this case, and prove two interesting properties that these TQFTs always have. In the case of the LMO invariant these properties amount to saying that the TQFT… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0602097v1-abstract-full').style.display = 'inline'; document.getElementById('math/0602097v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="math/0602097v1-abstract-full" style="display: none;"> The object of this paper is to define a subcategory of the category of 3-cobordisms to which invariants of rational homology 3-spheres should generalize. We specify the notion of Topological Quantum Field Theory (in the sense of Atiyah) to this case, and prove two interesting properties that these TQFTs always have. In the case of the LMO invariant these properties amount to saying that the TQFT is anomaly-free. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0602097v1-abstract-full').style.display = 'none'; document.getElementById('math/0602097v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 6 February, 2006; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2006. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">16 pages, 7 figures. Observation: 90% of the content has been previously part of math.GT/0508220 version 1, which now has been replaced with version 2, where the respective part was removed (except a few statements which were left for reference). The results here are independent of that paper and can be used also in differnt context from that of GT/0508220</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57M27 (primarily); 57R56; 81T45; 57R65 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/math/0601139">arXiv:math/0601139</a> <span> [<a href="https://arxiv.org/pdf/math/0601139">pdf</a>, <a href="https://arxiv.org/ps/math/0601139">ps</a>, <a href="https://arxiv.org/format/math/0601139">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> </div> <p class="title is-5 mathjax"> Is the Jones polynomial of a knot really a polynomial? </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Garoufalidis%2C+S">Stavros Garoufalidis</a>, <a href="/search/?searchtype=author&query=Le%2C+T+T+Q">Thang T. Q. Le</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="math/0601139v2-abstract-short" style="display: inline;"> The Jones polynomial of a knot in 3-space is a Laurent polynomial in $q$, with integer coefficients. Many people have pondered why is this so, and what is a proper generalization of the Jones polynomial for knots in other closed 3-manifolds. Our paper centers around this question. After reviewing several existing definitions of the Jones polynomial, we show that the Jones polynomial is really an… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0601139v2-abstract-full').style.display = 'inline'; document.getElementById('math/0601139v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="math/0601139v2-abstract-full" style="display: none;"> The Jones polynomial of a knot in 3-space is a Laurent polynomial in $q$, with integer coefficients. Many people have pondered why is this so, and what is a proper generalization of the Jones polynomial for knots in other closed 3-manifolds. Our paper centers around this question. After reviewing several existing definitions of the Jones polynomial, we show that the Jones polynomial is really an analytic function, in the sense of Habiro. Using this, we extend the holonomicity properties of the colored Jones function of a knot in 3-space to the case of a knot in an integer homology sphere, and we formulate an analogue of the AJ Conjecture. Our main tools are various integrality properties of topological quantum field theory invariants of links in 3-manifolds, manifested in Habiro's work on the colored Jones function.Revised version updating references on Witten-Reshetikhin-Turaev invariants. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0601139v2-abstract-full').style.display = 'none'; document.getElementById('math/0601139v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 January, 2006; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 7 January, 2006; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2006. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">13 pages and 12 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57N10 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/math/0512433">arXiv:math/0512433</a> <span> [<a href="https://arxiv.org/pdf/math/0512433">pdf</a>, <a href="https://arxiv.org/ps/math/0512433">ps</a>, <a href="https://arxiv.org/format/math/0512433">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> </div> <p class="title is-5 mathjax"> Strong Integrality of Quantum Invariants of 3-manifolds </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Le%2C+T+T+Q">Thang T. Q. Le</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="math/0512433v2-abstract-short" style="display: inline;"> We prove that the quantum SO(3)-invariant of an arbitrary 3-manifold $M$ is always an algebraic integer, if the order of the quantum parameter is co-prime with the order of the torsion part of $H_1(M,\BZ)$. An even stronger integrality, known as cyclotomic integrality, was established by Habiro for integral homology 3-spheres. Here we generalize Habiro's result to all rational homology 3-spheres… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0512433v2-abstract-full').style.display = 'inline'; document.getElementById('math/0512433v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="math/0512433v2-abstract-full" style="display: none;"> We prove that the quantum SO(3)-invariant of an arbitrary 3-manifold $M$ is always an algebraic integer, if the order of the quantum parameter is co-prime with the order of the torsion part of $H_1(M,\BZ)$. An even stronger integrality, known as cyclotomic integrality, was established by Habiro for integral homology 3-spheres. Here we generalize Habiro's result to all rational homology 3-spheres. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0512433v2-abstract-full').style.display = 'none'; document.getElementById('math/0512433v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 25 January, 2006; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 18 December, 2005; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2005. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">19 pages. Minor typos corrected</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57M25 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/math/0508220">arXiv:math/0508220</a> <span> [<a href="https://arxiv.org/pdf/math/0508220">pdf</a>, <a href="https://arxiv.org/ps/math/0508220">ps</a>, <a href="https://arxiv.org/format/math/0508220">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1007/s00220-007-0241-3">10.1007/s00220-007-0241-3 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> A TQFT associated to the LMO invariant of three-dimensional manifolds </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Cheptea%2C+D">Dorin Cheptea</a>, <a href="/search/?searchtype=author&query=Le%2C+T+T+Q">Thang T Q Le</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="math/0508220v2-abstract-short" style="display: inline;"> We construct a Topological Quantum Field Theory (in the sense of Atiyah) associated to the universal finite-type invariant of 3-dimensional manifolds, as a functor from the category of 3-dimensional manifolds with parametrized boundary, satisfying some additional conditions, to an algebraic-combinatorial category. It is built together with its truncations with respect to a natural grading, and w… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0508220v2-abstract-full').style.display = 'inline'; document.getElementById('math/0508220v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="math/0508220v2-abstract-full" style="display: none;"> We construct a Topological Quantum Field Theory (in the sense of Atiyah) associated to the universal finite-type invariant of 3-dimensional manifolds, as a functor from the category of 3-dimensional manifolds with parametrized boundary, satisfying some additional conditions, to an algebraic-combinatorial category. It is built together with its truncations with respect to a natural grading, and we prove that these TQFTs are non-degenerate and anomaly-free. The TQFT(s) induce(s) a (series of) representation(s) of a subgroup ${\cal L}_g$ of the Mapping Class Group that contains the Torelli group. The N=1 truncation produces a TQFT for the Casson-Walker-Lescop invariant. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0508220v2-abstract-full').style.display = 'none'; document.getElementById('math/0508220v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 6 February, 2006; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 12 August, 2005; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2005. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">28 pages, 13 postscript figures. Version 2 (Section 1 has been considerably shorten, and section 3 has been slightly shorten, since they will constitute a separate paper. Section 4, which contained only announce of results, has been suprimated; it will appear in detail elsewhere. Consequently some statements have been re-numbered. No mathematical changes have been made.)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57M27 (primarily); 57R56; 81T45; 81Q30; 81R50 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Commun.Math.Phys.272:601-634,2007 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/math/0508100">arXiv:math/0508100</a> <span> [<a href="https://arxiv.org/pdf/math/0508100">pdf</a>, <a href="https://arxiv.org/ps/math/0508100">ps</a>, <a href="https://arxiv.org/format/math/0508100">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.2140/gt.2011.15.2135">10.2140/gt.2011.15.2135 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Asymptotics of the colored Jones function of a knot </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Garoufalidis%2C+S">Stavros Garoufalidis</a>, <a href="/search/?searchtype=author&query=Le%2C+T+T+Q">Thang T. Q. Le</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="math/0508100v6-abstract-short" style="display: inline;"> To a knot in 3-space, one can associate a sequence of Laurent polynomials, whose $n$th term is the $n$th colored Jones polynomial. The paper is concerned with the asymptotic behavior of the value of the $n$th colored Jones polynomial at $e^{\a/n}$, when $\a$ is a fixed complex number and $n$ tends to infinity. We analyze this asymptotic behavior to all orders in $1/n$ when $\a$ is a sufficiently s… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0508100v6-abstract-full').style.display = 'inline'; document.getElementById('math/0508100v6-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="math/0508100v6-abstract-full" style="display: none;"> To a knot in 3-space, one can associate a sequence of Laurent polynomials, whose $n$th term is the $n$th colored Jones polynomial. The paper is concerned with the asymptotic behavior of the value of the $n$th colored Jones polynomial at $e^{\a/n}$, when $\a$ is a fixed complex number and $n$ tends to infinity. We analyze this asymptotic behavior to all orders in $1/n$ when $\a$ is a sufficiently small complex number. In addition, we give upper bounds for the coefficients and degree of the $n$th colored Jones polynomial, with applications to upper bounds in the Generalized Volume Conjecture. Work of Agol-Dunfield-Storm-W.Thurston implies that our bounds are asymptotically optimal. Moreover, we give results for the Generalized Volume Conjecture when $\a$ is near $2 蟺i$. Our proofs use crucially the cyclotomic expansion of the colored Jones function, due to Habiro. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0508100v6-abstract-full').style.display = 'none'; document.getElementById('math/0508100v6-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 31 August, 2011; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 4 August, 2005; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2005. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">31 pages, 13 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57N10; 57M25 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Geom. Topol. 15 (2011) 2135-2180 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/math/0507145">arXiv:math/0507145</a> <span> [<a href="https://arxiv.org/pdf/math/0507145">pdf</a>, <a href="https://arxiv.org/ps/math/0507145">ps</a>, <a href="https://arxiv.org/format/math/0507145">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Geometric Topology">math.GT</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Quantum Algebra">math.QA</span> </div> </div> <p class="title is-5 mathjax"> Finite type invariants of 3-manifolds </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/?searchtype=author&query=Le%2C+T+T+Q">Thang T. Q. Le</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="math/0507145v1-abstract-short" style="display: inline;"> This is a survey article on finite type invariants of 3-manifolds written for the Encyclopedia of Mathematical Physics to be published by Elsevier. </span> <span class="abstract-full has-text-grey-dark mathjax" id="math/0507145v1-abstract-full" style="display: none;"> This is a survey article on finite type invariants of 3-manifolds written for the Encyclopedia of Mathematical Physics to be published by Elsevier. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0507145v1-abstract-full').style.display = 'none'; document.getElementById('math/0507145v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 7 July, 2005; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2005. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">13 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57M27 </p> </li> </ol> <nav class="pagination is-small is-centered breathe-horizontal" role="navigation" aria-label="pagination"> <a href="" class="pagination-previous is-invisible">Previous </a> <a href="/search/?searchtype=author&query=Le%2C+T+Q&start=50" class="pagination-next" >Next </a> <ul class="pagination-list"> <li> <a href="/search/?searchtype=author&query=Le%2C+T+Q&start=0" class="pagination-link is-current" aria-label="Goto page 1">1 </a> </li> <li> <a href="/search/?searchtype=author&query=Le%2C+T+Q&start=50" class="pagination-link " aria-label="Page 2" aria-current="page">2 </a> </li> </ul> 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