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</div> <div class="control"> <button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <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/2501.14489">arXiv:2501.14489</a> <span> [<a href="https://arxiv.org/pdf/2501.14489">pdf</a>, <a href="https://arxiv.org/format/2501.14489">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="Differential Geometry">math.DG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> </div> </div> <p class="title is-5 mathjax"> On transverse $R$-covered minimal foliations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Barbot%2C+T">Thierry Barbot</a>, <a href="/search/math?searchtype=author&query=Fenley%2C+S+R">Sergio R. Fenley</a>, <a href="/search/math?searchtype=author&query=Potrie%2C+R">Rafael Potrie</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="2501.14489v1-abstract-short" style="display: inline;"> We study minimal transverse foliations which are $R$-covered. If in addition the dimension of the ambient manifold is $3$, and the foliations are Anosov foliations we give necessary and sufficient conditions for the intersected foliation to be the orbit foliation of an Anosov flow. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2501.14489v1-abstract-full" style="display: none;"> We study minimal transverse foliations which are $R$-covered. If in addition the dimension of the ambient manifold is $3$, and the foliations are Anosov foliations we give necessary and sufficient conditions for the intersected foliation to be the orbit foliation of an Anosov flow. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2501.14489v1-abstract-full').style.display = 'none'; document.getElementById('2501.14489v1-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 January, 2025; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2025. </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">42 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/2310.05176">arXiv:2310.05176</a> <span> [<a href="https://arxiv.org/pdf/2310.05176">pdf</a>, <a href="https://arxiv.org/format/2310.05176">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="Differential Geometry">math.DG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> </div> </div> <p class="title is-5 mathjax"> Intersection of transverse foliations in 3-manifolds: Hausdorff leafspace implies leafwise quasi-geodesic </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Fenley%2C+S+R">Sergio R. Fenley</a>, <a href="/search/math?searchtype=author&query=Potrie%2C+R">Rafael Potrie</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="2310.05176v3-abstract-short" style="display: inline;"> Let $\mathcal{F}_1$ and $\mathcal{F}_2$ be transverse two dimensional foliations with Gromov hyperbolic leaves in a closed 3-manifold $M$ whose fundamental group is not solvable, and let $\mathcal{G}$ be the one dimensional foliation obtained by intersection. We show that $\mathcal{G}$ is \emph{leafwise quasigeodesic} in $\mathcal{F}_1$ and $\mathcal{F}_2$ if and only if the foliation… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2310.05176v3-abstract-full').style.display = 'inline'; document.getElementById('2310.05176v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2310.05176v3-abstract-full" style="display: none;"> Let $\mathcal{F}_1$ and $\mathcal{F}_2$ be transverse two dimensional foliations with Gromov hyperbolic leaves in a closed 3-manifold $M$ whose fundamental group is not solvable, and let $\mathcal{G}$ be the one dimensional foliation obtained by intersection. We show that $\mathcal{G}$ is \emph{leafwise quasigeodesic} in $\mathcal{F}_1$ and $\mathcal{F}_2$ if and only if the foliation $\mathcal{G}_L$ induced by $\mathcal{G}$ in the universal cover $L$ of any leaf of $\mathcal{F}_1$ or $\mathcal{F}_2$ has Hausdorff leaf space. We end up with a discussion on the hypothesis of Gromov hyperbolicity of the leaves. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2310.05176v3-abstract-full').style.display = 'none'; document.getElementById('2310.05176v3-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 January, 2025; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 8 October, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 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">43 pages, 9 figures. Revision after referee's suggestions. To appear in Crelle's journal</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2303.14525">arXiv:2303.14525</a> <span> [<a href="https://arxiv.org/pdf/2303.14525">pdf</a>, <a href="https://arxiv.org/format/2303.14525">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="Differential Geometry">math.DG</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Dynamical Systems">math.DS</span> </div> </div> <p class="title is-5 mathjax"> Transverse minimal foliations on unit tangent bundles and applications </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Fenley%2C+S+R">Sergio R. Fenley</a>, <a href="/search/math?searchtype=author&query=Potrie%2C+R">Rafael Potrie</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="2303.14525v2-abstract-short" style="display: inline;"> We show that if $\mathcal{F}_1$ and $\mathcal{F}_2$ are two transverse minimal foliations on $M = T^1S$ then either they intersect in an Anosov foliation or there exists a Reeb-surface in the intersection foliation. The existence of a Reeb surface is incompatible with partially hyperbolic foliations so we deduce from this that certain partially hyperbolic diffeomorphisms in unit tangent bundles ar… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.14525v2-abstract-full').style.display = 'inline'; document.getElementById('2303.14525v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2303.14525v2-abstract-full" style="display: none;"> We show that if $\mathcal{F}_1$ and $\mathcal{F}_2$ are two transverse minimal foliations on $M = T^1S$ then either they intersect in an Anosov foliation or there exists a Reeb-surface in the intersection foliation. The existence of a Reeb surface is incompatible with partially hyperbolic foliations so we deduce from this that certain partially hyperbolic diffeomorphisms in unit tangent bundles are collapsed Anosov flows. We also conclude that every volume preserving partially hyperbolic diffeomorphism of a unit tangent bundle is ergodic. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2303.14525v2-abstract-full').style.display = 'none'; document.getElementById('2303.14525v2-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, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 25 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">64 pages, 20 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/2210.09238">arXiv:2210.09238</a> <span> [<a href="https://arxiv.org/pdf/2210.09238">pdf</a>, <a href="https://arxiv.org/format/2210.09238">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link 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> <p class="title is-5 mathjax"> Non R-covered Anosov flows in hyperbolic 3-manifolds are quasigeodesic </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Fenley%2C+S+R">Sergio R Fenley</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="2210.09238v1-abstract-short" style="display: inline;"> The main result is that if an Anosov flow in a closed hyperbolic three manifold is not R-covered, then the flow is a quasigeodesic flow. We also prove that if a hyperbolic three manifold supports an Anosov flow, then up to a double cover it supports a quasigeodesic flow. We prove the continuous extension property for the stable and unstable foliations of any Anosov flow in a closed hyperbolic thre… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2210.09238v1-abstract-full').style.display = 'inline'; document.getElementById('2210.09238v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2210.09238v1-abstract-full" style="display: none;"> The main result is that if an Anosov flow in a closed hyperbolic three manifold is not R-covered, then the flow is a quasigeodesic flow. We also prove that if a hyperbolic three manifold supports an Anosov flow, then up to a double cover it supports a quasigeodesic flow. We prove the continuous extension property for the stable and unstable foliations of any Anosov flow in a closed hyperbolic three manifold, and the existence of group invariant Peano curves associated with any such flow. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2210.09238v1-abstract-full').style.display = 'none'; document.getElementById('2210.09238v1-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 October, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 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">79 pages, 22 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> Primary: 57R30; 37E10; 37D20; Secondary: 53C12; 37C27; 37D05; 37C86 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2103.14630">arXiv:2103.14630</a> <span> [<a href="https://arxiv.org/pdf/2103.14630">pdf</a>, <a href="https://arxiv.org/format/2103.14630">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link 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> <p class="title is-5 mathjax"> Accessibility and ergodicity for collapsed Anosov flows </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Fenley%2C+S+R">Sergio R. Fenley</a>, <a href="/search/math?searchtype=author&query=Potrie%2C+R">Rafael Potrie</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="2103.14630v1-abstract-short" style="display: inline;"> We consider a class of partially hyperbolic diffeomorphisms introduced in [BFP] which is open and closed and contains all known examples. If in addition the diffeomorphism is non-wandering, then we show it is accessible unless it contains a su-torus. This implies that these systems are ergodic when they preserve volume, confirming a conjecture by Hertz-Hertz-Ures for this class of systems. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2103.14630v1-abstract-full" style="display: none;"> We consider a class of partially hyperbolic diffeomorphisms introduced in [BFP] which is open and closed and contains all known examples. If in addition the diffeomorphism is non-wandering, then we show it is accessible unless it contains a su-torus. This implies that these systems are ergodic when they preserve volume, confirming a conjecture by Hertz-Hertz-Ures for this class of systems. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.14630v1-abstract-full').style.display = 'none'; document.getElementById('2103.14630v1-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> 26 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">17 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/2102.02156">arXiv:2102.02156</a> <span> [<a href="https://arxiv.org/pdf/2102.02156">pdf</a>, <a href="https://arxiv.org/format/2102.02156">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link 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> <p class="title is-5 mathjax"> Partial hyperbolicity and pseudo-Anosov dynamics </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Fenley%2C+S+R">Sergio R. Fenley</a>, <a href="/search/math?searchtype=author&query=Potrie%2C+R">Rafael Potrie</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="2102.02156v3-abstract-short" style="display: inline;"> We show that if a hyperbolic 3-manifold admits a partially hyperbolic diffeomorphism then it also admits an Anosov flow. Moreover, we give a complete classification of partially hyperbolic diffeomorphism in hyperbolic 3-manifolds as well as partially hyperbolic diffeomorphisms in Seifert manifolds inducing pseudo-Anosov dynamics in the base. This classification is given in terms of the structure o… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2102.02156v3-abstract-full').style.display = 'inline'; document.getElementById('2102.02156v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2102.02156v3-abstract-full" style="display: none;"> We show that if a hyperbolic 3-manifold admits a partially hyperbolic diffeomorphism then it also admits an Anosov flow. Moreover, we give a complete classification of partially hyperbolic diffeomorphism in hyperbolic 3-manifolds as well as partially hyperbolic diffeomorphisms in Seifert manifolds inducing pseudo-Anosov dynamics in the base. This classification is given in terms of the structure of their center (branching) foliations and the notion of collapsed Anosov flows. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2102.02156v3-abstract-full').style.display = 'none'; document.getElementById('2102.02156v3-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 January, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 3 February, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 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">66 pages, 9 figures. Some changes to take into accounts suggestions by a referee. To appear in GAFA</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2008.06547">arXiv:2008.06547</a> <span> [<a href="https://arxiv.org/pdf/2008.06547">pdf</a>, <a href="https://arxiv.org/format/2008.06547">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link 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> <p class="title is-5 mathjax"> Collapsed Anosov flows and self orbit equivalences </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Barthelm%C3%A9%2C+T">Thomas Barthelm茅</a>, <a href="/search/math?searchtype=author&query=Fenley%2C+S+R">Sergio R. Fenley</a>, <a href="/search/math?searchtype=author&query=Potrie%2C+R">Rafael Potrie</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="2008.06547v3-abstract-short" style="display: inline;"> We propose a generalization of the concept of discretized Anosov flows that covers a wide class of partially hyperbolic diffeomorphisms in 3-manifolds, and that we call collapsed Anosov flows. They are related with Anosov flows via a self orbit equivalence of the flow. We show that all the examples constructed in a paper by Bonatti, Gogolev, Hammerlindl and the third author belong to this class, a… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2008.06547v3-abstract-full').style.display = 'inline'; document.getElementById('2008.06547v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2008.06547v3-abstract-full" style="display: none;"> We propose a generalization of the concept of discretized Anosov flows that covers a wide class of partially hyperbolic diffeomorphisms in 3-manifolds, and that we call collapsed Anosov flows. They are related with Anosov flows via a self orbit equivalence of the flow. We show that all the examples constructed in a paper by Bonatti, Gogolev, Hammerlindl and the third author belong to this class, and that it is an open and closed class among partially hyperbolic diffeomorphisms. We provide some equivalent definitions which may be more amenable to analysis and are useful in different situations. Conversely we describe the class of partially hyperbolic diffeomorphisms that are collapsed Anosov flows associated with certain types of Anosov flows. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2008.06547v3-abstract-full').style.display = 'none'; document.getElementById('2008.06547v3-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">v1</span> submitted 14 August, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 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">81 pages, 1 figure. This version clarifies some hypothesis and provides more details in some arguments. It also points out shortcuts to get some relevant instances of the results. Final version, to appear in Comm. Math. Helv</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2008.04871">arXiv:2008.04871</a> <span> [<a href="https://arxiv.org/pdf/2008.04871">pdf</a>, <a href="https://arxiv.org/format/2008.04871">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link 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/gt.2023.27.3095">10.2140/gt.2023.27.3095 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, Part II: Branching foliations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Barthelm%C3%A9%2C+T">Thomas Barthelm茅</a>, <a href="/search/math?searchtype=author&query=Fenley%2C+S+R">Sergio R. Fenley</a>, <a href="/search/math?searchtype=author&query=Frankel%2C+S">Steven Frankel</a>, <a href="/search/math?searchtype=author&query=Potrie%2C+R">Rafael Potrie</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="2008.04871v2-abstract-short" style="display: inline;"> We study $3$-dimensional partially hyperbolic diffeomorphisms that are homotopic to the identity, focusing on the geometry and dynamics of Burago and Ivanov's center stable and center unstable \emph{branching} foliations. This extends our study of the true foliations that appear in the dynamically coherent case (see \emph{Partially hyperbolic diffeomorphisms homotopic to the identity in dimension… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2008.04871v2-abstract-full').style.display = 'inline'; document.getElementById('2008.04871v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2008.04871v2-abstract-full" style="display: none;"> We study $3$-dimensional partially hyperbolic diffeomorphisms that are homotopic to the identity, focusing on the geometry and dynamics of Burago and Ivanov's center stable and center unstable \emph{branching} foliations. This extends our study of the true foliations that appear in the dynamically coherent case (see \emph{Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, Part I: The dynamically coherent case}, arxiv:1908.06227v3). We complete the classification of such diffeomorphisms in Seifert fibered manifolds. In hyperbolic manifolds, we show that any such diffeomorphism is either dynamically coherent and has a power that is a discretized Anosov flow, or is of a new potential class called a \emph{double translation}. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2008.04871v2-abstract-full').style.display = 'none'; document.getElementById('2008.04871v2-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 March, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 10 August, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 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">This is the second part of arxiv:1908.06227v1 that was split in two. This version has a new part 2-specific introduction and some improved explanations in the text. v2: This is the final accepted version. Some improvements in the text thanks to referees reports</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Geom. Topol. 27 (2023) 3095-3181 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1908.06227">arXiv:1908.06227</a> <span> [<a href="https://arxiv.org/pdf/1908.06227">pdf</a>, <a href="https://arxiv.org/format/1908.06227">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link 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> <p class="title is-5 mathjax"> Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, Part I: The dynamically coherent case </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Barthelm%C3%A9%2C+T">Thomas Barthelm茅</a>, <a href="/search/math?searchtype=author&query=Fenley%2C+S+R">Sergio R. Fenley</a>, <a href="/search/math?searchtype=author&query=Frankel%2C+S">Steven Frankel</a>, <a href="/search/math?searchtype=author&query=Potrie%2C+R">Rafael Potrie</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="1908.06227v4-abstract-short" style="display: inline;"> We study 3-dimensional dynamically coherent partially hyperbolic diffeomorphisms that are homotopic to the identity, focusing on the transverse geometry and topology of the center stable and center unstable foliations, and the dynamics within their leaves. We find a structural dichotomy for these foliations, which we use to show that every such diffeomorphism on a hyperbolic or Seifert fibered 3-m… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1908.06227v4-abstract-full').style.display = 'inline'; document.getElementById('1908.06227v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1908.06227v4-abstract-full" style="display: none;"> We study 3-dimensional dynamically coherent partially hyperbolic diffeomorphisms that are homotopic to the identity, focusing on the transverse geometry and topology of the center stable and center unstable foliations, and the dynamics within their leaves. We find a structural dichotomy for these foliations, which we use to show that every such diffeomorphism on a hyperbolic or Seifert fibered 3-manifold is leaf conjugate to the time one map of a (topological) Anosov flow. This proves a classification conjecture of Hertz-Hertz-Ures in hyperbolic 3-manifolds and in the homotopy class of the identity of Seifert manifolds. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1908.06227v4-abstract-full').style.display = 'none'; document.getElementById('1908.06227v4-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 March, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 16 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">v4: Final accepted version. Some improvement in the text thanks to referees</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 37D30; 57R30; 37C15; 57M50; 37D20 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1505.07999">arXiv:1505.07999</a> <span> [<a href="https://arxiv.org/pdf/1505.07999">pdf</a>, <a href="https://arxiv.org/ps/1505.07999">ps</a>, <a href="https://arxiv.org/format/1505.07999">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link 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> <p class="title is-5 mathjax"> Counting periodic orbits of Anosov flows in free homotopy classes </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Barthelm%C3%A9%2C+T">Thomas Barthelm茅</a>, <a href="/search/math?searchtype=author&query=Fenley%2C+S+R">Sergio R. Fenley</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="1505.07999v1-abstract-short" style="display: inline;"> The main result of this article is that if a $3$-manifold $M$ supports an Anosov flow, then the number of conjugacy classes in the fundamental group of $M$ grows exponentially fast with the length of the shortest orbit representative, hereby answering a question raised by Plante and Thurston in 1972. In fact we show that, when the flow is transitive, the exponential growth rate is exactly the topo… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1505.07999v1-abstract-full').style.display = 'inline'; document.getElementById('1505.07999v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1505.07999v1-abstract-full" style="display: none;"> The main result of this article is that if a $3$-manifold $M$ supports an Anosov flow, then the number of conjugacy classes in the fundamental group of $M$ grows exponentially fast with the length of the shortest orbit representative, hereby answering a question raised by Plante and Thurston in 1972. In fact we show that, when the flow is transitive, the exponential growth rate is exactly the topological entropy of the flow. We also show that taking only the shortest orbit representatives in each conjugacy classes still yields Bowen's version of the measure of maximal entropy. These results are achieved by obtaining counting results on the growth rate of the number of periodic orbits inside a free homotopy class. In the first part of the article, we also construct many examples of Anosov flows having some finite and some infinite free homotopy classes of periodic orbits, and we also give a characterization of algebraic Anosov flows as the only $\mathbb{R}$-covered Anosov flows up to orbit equivalence that do not admit at least one infinite free homotopy class of periodic orbits. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1505.07999v1-abstract-full').style.display = 'none'; document.getElementById('1505.07999v1-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, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 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">44 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/1405.4542">arXiv:1405.4542</a> <span> [<a href="https://arxiv.org/pdf/1405.4542">pdf</a>, <a href="https://arxiv.org/ps/1405.4542">ps</a>, <a href="https://arxiv.org/format/1405.4542">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="Dynamical Systems">math.DS</span> </div> </div> <p class="title is-5 mathjax"> Quasigeodesic pseudo-Anosov flows in hyperbolic 3-manifolds and connections with large scale geometry </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Fenley%2C+S+R">Sergio R Fenley</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="1405.4542v2-abstract-short" style="display: inline;"> In this article we obtain a simple topological and dynamical systems condition which is necessary and sufficient for an arbitrary pseudo-Anosov flow in a closed, hyperbolic three manifold to be quasigeodesic. Quasigeodesic means that orbits are efficient in measuring length up to a bounded multiplicative distortion when lifted to the universal cover. We prove that such flows are quasigeodesic if a… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1405.4542v2-abstract-full').style.display = 'inline'; document.getElementById('1405.4542v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1405.4542v2-abstract-full" style="display: none;"> In this article we obtain a simple topological and dynamical systems condition which is necessary and sufficient for an arbitrary pseudo-Anosov flow in a closed, hyperbolic three manifold to be quasigeodesic. Quasigeodesic means that orbits are efficient in measuring length up to a bounded multiplicative distortion when lifted to the universal cover. We prove that such flows are quasigeodesic if and only if there is an upper bound, depending only on the flow, to the number of orbits which are freely homotopic to an arbitrary closed orbit of the flow. The main ingredient is a proof that under the boundedness condition, the fundamental group of the manifold acts as a uniform convergence group on a flow ideal boundary of the universal cover. We also construct a flow ideal compactification of the universal cover and prove it is equivariantly homeomorphic to the Gromov compatification. This implies the quasigeodesic behavior of the flow. The flow ideal boundary and flow ideal compactification are constructed using only the structure of the flow. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1405.4542v2-abstract-full').style.display = 'none'; document.getElementById('1405.4542v2-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 June, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 18 May, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2014. </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">65 pages, 20 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57M50; 37D20; 37D50; 37C85 (Primary); 20D67; 32D45; 57M60; 73D05 (Secondary) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1403.0310">arXiv:1403.0310</a> <span> [<a href="https://arxiv.org/pdf/1403.0310">pdf</a>, <a href="https://arxiv.org/ps/1403.0310">ps</a>, <a href="https://arxiv.org/format/1403.0310">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="Dynamical Systems">math.DS</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/etds.2014.97">10.1017/etds.2014.97 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Diversified homotopic behavior of closed orbits of some R-covered Anosov flows </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Fenley%2C+S+R">Sergio R. Fenley</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="1403.0310v2-abstract-short" style="display: inline;"> We produce infinitely many examples of Anosov flows in closed 3-manifolds where the set of periodic orbits is partitioned into two infinite subsets. In one subset every closed orbit is freely homotopic to infinitely other closed orbits of the flow. In the other subset every closed orbit is freely homotopic to only one other closed orbit. The examples are obtained by Dehn surgery on geodesic flows.… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1403.0310v2-abstract-full').style.display = 'inline'; document.getElementById('1403.0310v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1403.0310v2-abstract-full" style="display: none;"> We produce infinitely many examples of Anosov flows in closed 3-manifolds where the set of periodic orbits is partitioned into two infinite subsets. In one subset every closed orbit is freely homotopic to infinitely other closed orbits of the flow. In the other subset every closed orbit is freely homotopic to only one other closed orbit. The examples are obtained by Dehn surgery on geodesic flows. The manifolds are toroidal and have Seifert fibered pieces and atoroidal pieces in their torus decompositions. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1403.0310v2-abstract-full').style.display = 'none'; document.getElementById('1403.0310v2-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 August, 2014; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 2 March, 2014; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2014. </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">Second version has new section 2 with previous results and definitions about Anosov flows, R-covered Anosov flows, Dehn surgery and hyperbolic/flow Dehn surgery. 11 pages, 1 figure</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 37D05; 37D20; 53C12; 53D25; 37C27 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Ergod. Th. Dynam. Sys. 36 (2016) 767-780 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1211.7327">arXiv:1211.7327</a> <span> [<a href="https://arxiv.org/pdf/1211.7327">pdf</a>, <a href="https://arxiv.org/ps/1211.7327">ps</a>, <a href="https://arxiv.org/format/1211.7327">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="Dynamical Systems">math.DS</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/etds.2014.9">10.1017/etds.2014.9 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Classification and rigidity of totally periodic pseudo-Anosov flows in graph manifolds </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Barbot%2C+T">Thierry Barbot</a>, <a href="/search/math?searchtype=author&query=Fenley%2C+S+R">Sergio R. Fenley</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="1211.7327v1-abstract-short" style="display: inline;"> In this article we analyze totally periodic pseudo-Anosov flows in graph three manifolds. This means that in each Seifert fibered piece of the torus decomposition, the free homotopy class of regular fibers has a finite power which is also a finite power of the free homotopy class of a closed orbit of the flow. We show that each such flow is topologically equivalent to one of the model pseudo-Anoso… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1211.7327v1-abstract-full').style.display = 'inline'; document.getElementById('1211.7327v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1211.7327v1-abstract-full" style="display: none;"> In this article we analyze totally periodic pseudo-Anosov flows in graph three manifolds. This means that in each Seifert fibered piece of the torus decomposition, the free homotopy class of regular fibers has a finite power which is also a finite power of the free homotopy class of a closed orbit of the flow. We show that each such flow is topologically equivalent to one of the model pseudo-Anosov flows which we constructed in a previous article. A model pseudo-Anosov flow is obtained by glueing standard neighborhoods of Birkhoff annuli and perhaps doing Dehn surgery on certain orbits. We also show that two model flows on the same graph manifold are isotopically equivalent (ie. there is a isotopy of the manifold mapping the oriented orbits of the first flow to the oriented orbits of the second flow) if and only if they have the same topological and dynamical data in the collection of standard neighborhoods of the Birkhoff annuli. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1211.7327v1-abstract-full').style.display = 'none'; document.getElementById('1211.7327v1-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 November, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 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">29 pages, 6 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 37D20; 37D50 (Primary) 57M60; 57R30 (Secondary) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1208.6487">arXiv:1208.6487</a> <span> [<a href="https://arxiv.org/pdf/1208.6487">pdf</a>, <a href="https://arxiv.org/ps/1208.6487">ps</a>, <a href="https://arxiv.org/format/1208.6487">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link 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/10.1112/jtopol/jtt041">10.1112/jtopol/jtt041 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Knot theory of R-covered Anosov flows: homotopy versus isotopy of closed orbits </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Barthelm%C3%A9%2C+T">Thomas Barthelm茅</a>, <a href="/search/math?searchtype=author&query=Fenley%2C+S+R">Sergio R. Fenley</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="1208.6487v1-abstract-short" style="display: inline;"> In this article, we study the knots realized by periodic orbits of R-covered Anosov flows in compact 3-manifolds. We show that if two orbits are freely homotopic then in fact they are isotopic. We show that lifts of periodic orbits to the universal cover are unknotted. When the manifold is atoroidal, we deduce some finer properties regarding the existence of embedded cylinders connecting two given… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1208.6487v1-abstract-full').style.display = 'inline'; document.getElementById('1208.6487v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1208.6487v1-abstract-full" style="display: none;"> In this article, we study the knots realized by periodic orbits of R-covered Anosov flows in compact 3-manifolds. We show that if two orbits are freely homotopic then in fact they are isotopic. We show that lifts of periodic orbits to the universal cover are unknotted. When the manifold is atoroidal, we deduce some finer properties regarding the existence of embedded cylinders connecting two given homotopic orbits. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1208.6487v1-abstract-full').style.display = 'none'; document.getElementById('1208.6487v1-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, 2012; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 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">20 pages, 9 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/1006.4525">arXiv:1006.4525</a> <span> [<a href="https://arxiv.org/pdf/1006.4525">pdf</a>, <a href="https://arxiv.org/format/1006.4525">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/etds.2019.56">10.1017/etds.2019.56 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Endperiodic Automorphisms of Surfaces and Foliations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Cantwell%2C+J">John Cantwell</a>, <a href="/search/math?searchtype=author&query=Conlon%2C+L">Lawrence Conlon</a>, <a href="/search/math?searchtype=author&query=Fenley%2C+S+R">Sergio R. Fenley</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="1006.4525v8-abstract-short" style="display: inline;"> We extend the unpublished work of M. Handel and R. Miller on the classification, up to isotopy, of endperiodic automorphisms of surfaces. We give the Handel-Miller construction of the geodesic laminations, give an axiomatic theory for pseudo-geodesic lamaniations, show the geodesic laminations satisfy the axioms, and prove that paeudo-geodesic laminations satisfying our axioms are ambiently isotop… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1006.4525v8-abstract-full').style.display = 'inline'; document.getElementById('1006.4525v8-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1006.4525v8-abstract-full" style="display: none;"> We extend the unpublished work of M. Handel and R. Miller on the classification, up to isotopy, of endperiodic automorphisms of surfaces. We give the Handel-Miller construction of the geodesic laminations, give an axiomatic theory for pseudo-geodesic lamaniations, show the geodesic laminations satisfy the axioms, and prove that paeudo-geodesic laminations satisfying our axioms are ambiently isotopic to the geodesic laminations. The axiomatic approach allows us to show that the given endperiodic automorphism is isotopic to a smooth endperiodic automorphism preserving smooth laminations ambiently isotopic to the original ones. Using the axioms, we also prove the "transfer theorem" for foliations of 3-manifolds., namely that, if two depth one foliations are transverse to a common one-dimensional foliation whose monodromy on the noncompact leaves of the first foliation exhibits the nice dynamics of Handel-Miller theory, then the transverse one-dimensional foliation also induces monodromy on the noncompact leaves of the second foliation exhibiting the same nice dynamics. Our theory also applies to surfaces with infinitely many ends. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1006.4525v8-abstract-full').style.display = 'none'; document.getElementById('1006.4525v8-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 July, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 23 June, 2010; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 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">Added Sergio Fenley as author. Moved material from Section 12.6 to a new Section 6.7. Rewrote Section 7. Deleted material from Section 6.1 and combined Sections 6.1 and 6.2 into new Section 6.1. Rewrote Section 4.6. Corrected typos and errors and improved exposition</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 57R30 (primary); 37E30 (secondary) </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Ergod. Th. Dynam. Sys. 41 (2021) 66-212 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0705.2735">arXiv:0705.2735</a> <span> [<a href="https://arxiv.org/pdf/0705.2735">pdf</a>, <a href="https://arxiv.org/ps/0705.2735">ps</a>, <a href="https://arxiv.org/format/0705.2735">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="Dynamical Systems">math.DS</span> </div> </div> <p class="title is-5 mathjax"> Rigidity of pseudo-Anosov flows transverse to R-covered foliations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Fenley%2C+S+R">Sergio R Fenley</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="0705.2735v1-abstract-short" style="display: inline;"> A foliation is R-covered if the leaf space in the universal cover is homeomorphic to the real numbers. We show that, up to topological conjugacy, there are at most two pseudo-Anosov flows transverse to such a foliation. If there are two, then the foliation is weakly conjugate to the the stable foliation of an R-covered Anosov flow. The proof uses the universal circle to R-covered foliations. </span> <span class="abstract-full has-text-grey-dark mathjax" id="0705.2735v1-abstract-full" style="display: none;"> A foliation is R-covered if the leaf space in the universal cover is homeomorphic to the real numbers. We show that, up to topological conjugacy, there are at most two pseudo-Anosov flows transverse to such a foliation. If there are two, then the foliation is weakly conjugate to the the stable foliation of an R-covered Anosov flow. The proof uses the universal circle to R-covered foliations. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0705.2735v1-abstract-full').style.display = 'none'; document.getElementById('0705.2735v1-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 May, 2007; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 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">20 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 37C15; 37D20; 37C85; 37D50 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/math/0507153">arXiv:math/0507153</a> <span> [<a href="https://arxiv.org/pdf/math/0507153">pdf</a>, <a href="https://arxiv.org/ps/math/0507153">ps</a>, <a href="https://arxiv.org/format/math/0507153">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="Dynamical Systems">math.DS</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.2012.16.1">10.2140/gt.2012.16.1 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Ideal boundaries of pseudo-Anosov flows and uniform convergence groups, with connections and applications to large scale geometry </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Fenley%2C+S+R">Sergio R. Fenley</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/0507153v4-abstract-short" style="display: inline;"> Given a general pseudo-Anosov flow in a three manifold, the orbit space of the lifted flow to the universal cover is homeomorphic to an open disk. We compactify this orbit space with an ideal circle boundary. If there are no perfect fits between stable and unstable leaves and the flow is not topologically conjugate to a suspension Anosov flow, we then show: The ideal circle of the orbit space has… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0507153v4-abstract-full').style.display = 'inline'; document.getElementById('math/0507153v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="math/0507153v4-abstract-full" style="display: none;"> Given a general pseudo-Anosov flow in a three manifold, the orbit space of the lifted flow to the universal cover is homeomorphic to an open disk. We compactify this orbit space with an ideal circle boundary. If there are no perfect fits between stable and unstable leaves and the flow is not topologically conjugate to a suspension Anosov flow, we then show: The ideal circle of the orbit space has a natural quotient space which is a sphere and is a dynamical systems ideal boundary for a compactification of the universal cover of the manifold. The main result is that the fundamental group acts on the flow ideal boundary as a uniform convergence group. Using a theorem of Bowditch, this yields a proof that the fundamental group of the manifold is Gromov hyperbolic and it shows that the action of the fundamental group on the flow ideal boundary is conjugate to the action on the Gromov ideal boundary. This implies that pseudo-Anosov flows without perfect fits are quasigeodesic flows and we show that the stable/unstable foliations of these flows are quasi-isometric. Finally we apply these results to foliations: if a foliation is R-covered or with one sided branching in an atoroidal three manifold then the results above imply that the leaves of the foliation in the universal cover extend continuously to the sphere at infinity. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0507153v4-abstract-full').style.display = 'none'; document.getElementById('math/0507153v4-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 September, 2011; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 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">69 pages. Major revision, more explanations and simplified some simplified proofs. Detailed explanations of scalloped regions, parabolic points and perfect fit horoballs. 22 figures (3 new figures)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> Primary: 37D20; 53C23; 57R30; 37C85; Secondary: 57M50; 37D50; 58D19 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Geom. Topol. 16 (2012) 1-110 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/math/0502330">arXiv:math/0502330</a> <span> [<a href="https://arxiv.org/pdf/math/0502330">pdf</a>, <a href="https://arxiv.org/ps/math/0502330">ps</a>, <a href="https://arxiv.org/format/math/0502330">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="Dynamical Systems">math.DS</span> </div> </div> <p class="title is-5 mathjax"> Geometry of foliations and flows I: Almost transverse pseudo-Anosov flows and asymptotic behavior of foliations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Fenley%2C+S+R">Sergio R. Fenley</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/0502330v2-abstract-short" style="display: inline;"> Let F be a foliation in a closed 3-manifold with negatively curved fundamental group and suppose that F is almost transverse to a quasigeodesic pseudo-Anosov flow. We show that the leaves of the foliation in the universal cover extend continuously to the sphere at infinity, hence the limit sets are continuous images of the circle. One important corollary is that if F is a Reebless finite depth f… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0502330v2-abstract-full').style.display = 'inline'; document.getElementById('math/0502330v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="math/0502330v2-abstract-full" style="display: none;"> Let F be a foliation in a closed 3-manifold with negatively curved fundamental group and suppose that F is almost transverse to a quasigeodesic pseudo-Anosov flow. We show that the leaves of the foliation in the universal cover extend continuously to the sphere at infinity, hence the limit sets are continuous images of the circle. One important corollary is that if F is a Reebless finite depth foliation in a hyperbolic manifold, then it has the continuous extension property. Such finite depth foliations exist whenever the second Betti number is non zero. The result also applies to other classes of foliations, including a large class of foliations where all leaves are dense and infinitely many examples with one sided branching. One key tool is a detailed understanding of asymptotic properties of almost pseudo-Anosov singular 1-dimensional foliations in the leaves of F lifted to the universal cover. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0502330v2-abstract-full').style.display = 'none'; document.getElementById('math/0502330v2-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 15 February, 2005; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 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">56 pages, 17 figures. Rearranged presentation, more explanations</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> Primary: 53C23; 57R30; 37D20; Secondary: 57M99; 53C12; 32Q05; 57M50 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/math/0210482">arXiv:math/0210482</a> <span> [<a href="https://arxiv.org/pdf/math/0210482">pdf</a>, <a href="https://arxiv.org/ps/math/0210482">ps</a>, <a href="https://arxiv.org/format/math/0210482">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"> Laminar free hyperbolic 3-manifolds </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Fenley%2C+S+R">Sergio R. Fenley</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/0210482v1-abstract-short" style="display: inline;"> We analyse the existence question for essential laminations in 3-manifolds. The purpose is to prove that there are infinitely many closed hyperbolic 3-manifolds which do not admit essential laminations. This answers in the negative a question posed by Gabai and Oertel. The proof is obtained by analysing certain group actions on trees and showing that certain 3-manifold groups only have trivial a… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0210482v1-abstract-full').style.display = 'inline'; document.getElementById('math/0210482v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="math/0210482v1-abstract-full" style="display: none;"> We analyse the existence question for essential laminations in 3-manifolds. The purpose is to prove that there are infinitely many closed hyperbolic 3-manifolds which do not admit essential laminations. This answers in the negative a question posed by Gabai and Oertel. The proof is obtained by analysing certain group actions on trees and showing that certain 3-manifold groups only have trivial actions on trees. In general the trees are neither simplicial nor metric. There are corollaries concerning the existence question for Reebless foliations and pseudo-Anosov flows. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/0210482v1-abstract-full').style.display = 'none'; document.getElementById('math/0210482v1-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 October, 2002; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2002. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 20E08; 20F65; 57M50; 57M60 (primary) 37R85; 57R30 (secondary) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/math/9411204">arXiv:math/9411204</a> <span> [<a href="https://arxiv.org/pdf/math/9411204">pdf</a>, <a href="https://arxiv.org/ps/math/9411204">ps</a>, <a href="https://arxiv.org/format/math/9411204">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="Dynamical Systems">math.DS</span> </div> </div> <p class="title is-5 mathjax"> The structure of branching in Anosov flows of 3-manifolds </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Fenley%2C+S+R">Sergio R. Fenley</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/9411204v1-abstract-short" style="display: inline;"> In this article we study the topological structure of the lifts to the universal of the stable and unstable foliations of $3$-dimensional Anosov flows. In particular we consider the case when these foliations do not have Hausdorff leaf space. We completely determine the structure of the set of non separated leaves from a given leaf in one of these foliations. As a consequence of this suspensions… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/9411204v1-abstract-full').style.display = 'inline'; document.getElementById('math/9411204v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="math/9411204v1-abstract-full" style="display: none;"> In this article we study the topological structure of the lifts to the universal of the stable and unstable foliations of $3$-dimensional Anosov flows. In particular we consider the case when these foliations do not have Hausdorff leaf space. We completely determine the structure of the set of non separated leaves from a given leaf in one of these foliations. As a consequence of this suspensions are characterized, up to topological conjugacy, as the only $3$-dimensional Anosov flows without freely homotopic closed orbits. Furthermore the structure of branching is related to the topology of the manifold: if there are infinitely many leaves not separated from each other, then there is an incompressible torus transverse to the flow. Transitivity is not assumed for these results. Finally, if the manifold has negatively curved fundamental group we derive some important properties of the limit sets of leaves in the universal cover. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('math/9411204v1-abstract-full').style.display = 'none'; document.getElementById('math/9411204v1-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> 28 November, 1994; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 1994. </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, uuencoded tar file, uses 2 included macro files, contains 17 Encapsulated PostScript illustrations, 45 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> formerly cd-hg/9411001 </p> </li> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul class="nav-spaced"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 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