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name="searchtype"><option value="all">All fields</option><option value="title">Title</option><option selected value="author">Author(s)</option><option value="abstract">Abstract</option><option value="comments">Comments</option><option value="journal_ref">Journal reference</option><option value="acm_class">ACM classification</option><option value="msc_class">MSC classification</option><option value="report_num">Report number</option><option value="paper_id">arXiv identifier</option><option value="doi">DOI</option><option value="orcid">ORCID</option><option value="license">License (URI)</option><option value="author_id">arXiv author ID</option><option value="help">Help pages</option><option value="full_text">Full text</option></select> <input id="query" name="query" type="text" value="Brum, J"> <ul id="abstracts"><li><input checked id="abstracts-0" name="abstracts" type="radio" value="show"> <label for="abstracts-0">Show abstracts</label></li><li><input id="abstracts-1" name="abstracts" type="radio" value="hide"> <label for="abstracts-1">Hide abstracts</label></li></ul> </div> <div class="box field is-grouped is-grouped-multiline level-item"> <div class="control"> <span class="select is-small"> <select id="size" name="size"><option value="25">25</option><option selected value="50">50</option><option value="100">100</option><option value="200">200</option></select> </span> <label for="size">results per page</label>. </div> <div class="control"> <label for="order">Sort results by</label> <span class="select is-small"> <select id="order" name="order"><option selected value="-announced_date_first">Announcement date (newest first)</option><option value="announced_date_first">Announcement date (oldest first)</option><option value="-submitted_date">Submission date (newest first)</option><option value="submitted_date">Submission date (oldest first)</option><option value="">Relevance</option></select> </span> </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/2306.03846">arXiv:2306.03846</a> <span> [<a href="https://arxiv.org/pdf/2306.03846">pdf</a>, <a href="https://arxiv.org/ps/2306.03846">ps</a>, <a href="https://arxiv.org/format/2306.03846">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Group Theory">math.GR</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"> A realisation result for moduli spaces of group actions on the line </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Brum%2C+J">Joaqu铆n Brum</a>, <a href="/search/math?searchtype=author&query=Bon%2C+N+M">Nicol谩s Matte Bon</a>, <a href="/search/math?searchtype=author&query=Rivas%2C+C">Crist贸bal Rivas</a>, <a href="/search/math?searchtype=author&query=Triestino%2C+M">Michele Triestino</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="2306.03846v4-abstract-short" style="display: inline;"> Given a finitely generated group $G$, the possible actions of $G$ on the real line (without global fixed points), considered up to semi-conjugacy, can be encoded by the space of orbits of a flow on a compact space $(Y, 桅)$ naturally associated with $G$ and uniquely defined up to flow equivalence, that we call the \emph{Deroin space} of $G$. We show a realisation result: every expansive flow… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.03846v4-abstract-full').style.display = 'inline'; document.getElementById('2306.03846v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2306.03846v4-abstract-full" style="display: none;"> Given a finitely generated group $G$, the possible actions of $G$ on the real line (without global fixed points), considered up to semi-conjugacy, can be encoded by the space of orbits of a flow on a compact space $(Y, 桅)$ naturally associated with $G$ and uniquely defined up to flow equivalence, that we call the \emph{Deroin space} of $G$. We show a realisation result: every expansive flow $(Y, 桅)$ on a compact metrisable space of topological dimension 1, satisfying some mild additional assumptions, arises as the Deroin space of a finitely generated group. This is proven by identifying the Deroin space of an explicit family of groups acting on suspension flows of subshifts, which is a variant of a construction introduced by the second and fourth authors. This result provides a source of examples of finitely generated groups satisfying various new phenomena for actions on the line, related to their rigidity/flexibility properties and to the structure of (path-)connected components of the space of actions. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2306.03846v4-abstract-full').style.display = 'none'; document.getElementById('2306.03846v4-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 September, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 6 June, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 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">32 pages; v4: minor corrections and references updated, final version to appear in the Journal of Topology</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2209.00091">arXiv:2209.00091</a> <span> [<a href="https://arxiv.org/pdf/2209.00091">pdf</a>, <a href="https://arxiv.org/format/2209.00091">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Group Theory">math.GR</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"> Solvable Groups and Affine Actions on the Line </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Brum%2C+J">Joaqu铆n Brum</a>, <a href="/search/math?searchtype=author&query=Bon%2C+N+M">Nicol谩s Matte Bon</a>, <a href="/search/math?searchtype=author&query=Rivas%2C+C">Crist贸bal Rivas</a>, <a href="/search/math?searchtype=author&query=Triestino%2C+M">Michele Triestino</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="2209.00091v2-abstract-short" style="display: inline;"> We prove a structural result for orientation-preserving actions of finitely generated solvable groups on real intervals, considered up to semi-conjugacy. As applications we obtain new answers to a problem first considered by J. F. Plante, which asks under which conditions an action of a solvable group on a real interval is semi-conjugate to an action on the line by affine transformations. We show… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2209.00091v2-abstract-full').style.display = 'inline'; document.getElementById('2209.00091v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2209.00091v2-abstract-full" style="display: none;"> We prove a structural result for orientation-preserving actions of finitely generated solvable groups on real intervals, considered up to semi-conjugacy. As applications we obtain new answers to a problem first considered by J. F. Plante, which asks under which conditions an action of a solvable group on a real interval is semi-conjugate to an action on the line by affine transformations. We show that this is always the case for actions by $C^1$ diffeomorphisms on closed intervals. For arbitrary actions by homeomorphisms, for which this result is no longer true (as shown by Plante), we show that a semi-conjugacy to an affine action still exists in a local sense, at the level of germs near the endpoints. Finally for a vast class of solvable groups, including all solvable linear groups, we show that the family of affine actions on the line is robust, in the sense that any action by homeomorphisms on the line which is sufficiently close to an affine action must be semi-conjugate to an affine action. This robustness fails for general solvable groups, as illustrated by a counterexample. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2209.00091v2-abstract-full').style.display = 'none'; document.getElementById('2209.00091v2-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 September, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 31 August, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 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">v2 incorporates suggestions of the referees (discussions of examples), and changes needed after the revision of the companion work arXiv:2104.14678; 39 pages, 1 figure</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 20F16; 37C85; 20E08; 20F60; 57M60 (primary) 37E05; 37B05 (secondary) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2104.14678">arXiv:2104.14678</a> <span> [<a href="https://arxiv.org/pdf/2104.14678">pdf</a>, <a href="https://arxiv.org/format/2104.14678">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Group Theory">math.GR</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"> Locally moving groups and laminar actions on the line </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Brum%2C+J">Joaqu铆n Brum</a>, <a href="/search/math?searchtype=author&query=Bon%2C+N+M">Nicol谩s Matte Bon</a>, <a href="/search/math?searchtype=author&query=Rivas%2C+C">Crist贸bal Rivas</a>, <a href="/search/math?searchtype=author&query=Triestino%2C+M">Michele Triestino</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="2104.14678v3-abstract-short" style="display: inline;"> We prove various results that, given a sufficiently rich subgroup $G$ of the group of homeomorphisms on the real line, describe the structure of the other possible actions of $G$ on the line, and address under which conditions such actions must be semi-conjugate to the natural defining action of $G$. The main assumption is that $G$ should be locally moving, meaning that for every open interval the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2104.14678v3-abstract-full').style.display = 'inline'; document.getElementById('2104.14678v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2104.14678v3-abstract-full" style="display: none;"> We prove various results that, given a sufficiently rich subgroup $G$ of the group of homeomorphisms on the real line, describe the structure of the other possible actions of $G$ on the line, and address under which conditions such actions must be semi-conjugate to the natural defining action of $G$. The main assumption is that $G$ should be locally moving, meaning that for every open interval the subgroup of elements fixing pointwise its complement, acts on it without fixed points. We show that when $G$ is a locally moving group, every $C^1$ action of $G$ on the real line is semi-conjugate to its standard action or to a non-faithful action. The situation is much wilder when considering actions by homeomorphisms: for a large class of groups, we describe uncountably many conjugacy classes of faithful minimal actions. Next, we prove structure theorems for $C^0$ actions, based on the study of laminar actions, which are actions on the line preserving a lamination. When $G$ is a group of homeomorphisms of the line acting minimally, and with a non-trivial compactly supported element, then any faithful minimal action of $G$ on the line is either laminar or conjugate to its standard action. Moreover, when $G$ is a locally moving group with a suitable finite generation condition, for any faithful minimal laminar action there is a map from the lamination to the line, called a horograding, which is equivariant with respect to the action on the lamination and the standard one, and with some extra suitable conditions. This establishes a tight relation between all minimal actions on the line of such groups, and their standard actions. Finally, based on an analysis of the space of harmonic actions, we show that for a large class of locally moving groups, the standard action is locally rigid, in the sense that sufficiently small perturbations in the compact-open topology give semi-conjugate actions. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2104.14678v3-abstract-full').style.display = 'none'; document.getElementById('2104.14678v3-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 November, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 29 April, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 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">205 pages, 11 figures; v2 is a major revision after report: title changed (previously 'Locally moving groups acting on the line and $\mathbb{R}$-focal actions'), structure reworked (chapters organized into 3 parts, each devoted to a single main theorem), many results strengthend to nearly optimal statements (requiring different approaches), digressions removed. To appear as an Ast茅risque volume</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> Primary 37C85. Secondary 20E08; 20F60; 37E05; 37B05; 57M60 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2006.12345">arXiv:2006.12345</a> <span> [<a href="https://arxiv.org/pdf/2006.12345">pdf</a>, <a href="https://arxiv.org/format/2006.12345">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> </div> </div> <p class="title is-5 mathjax"> Generic Rotation Sets in Hyperbolic Surfaces </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Alonso%2C+J">J. Alonso</a>, <a href="/search/math?searchtype=author&query=Brum%2C+J">J. Brum</a>, <a href="/search/math?searchtype=author&query=Passeggi%2C+A">A. Passeggi</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="2006.12345v1-abstract-short" style="display: inline;"> We show that for generic homeomorphisms homotopic to the identity in a closed and oriented surface of genus $g>1$, the rotation set is given by a union of at most $2^{5g-3}$ convex sets. Examples showing the sharpness for this asymptotic order are provided. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2006.12345v1-abstract-full" style="display: none;"> We show that for generic homeomorphisms homotopic to the identity in a closed and oriented surface of genus $g>1$, the rotation set is given by a union of at most $2^{5g-3}$ convex sets. Examples showing the sharpness for this asymptotic order are provided. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2006.12345v1-abstract-full').style.display = 'none'; document.getElementById('2006.12345v1-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, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2020. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2005.09050">arXiv:2005.09050</a> <span> [<a href="https://arxiv.org/pdf/2005.09050">pdf</a>, <a href="https://arxiv.org/format/2005.09050">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> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="General Topology">math.GN</span> </div> </div> <p class="title is-5 mathjax"> Topology of leaves for minimal laminations by non-simply connected hyperbolic surfaces </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Alvarez%2C+S">S茅bastien Alvarez</a>, <a href="/search/math?searchtype=author&query=Brum%2C+J">Joaqu铆n Brum</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="2005.09050v2-abstract-short" style="display: inline;"> We give the topological obstructions to be a leaf in a minimal lamination by hyperbolic surfaces whose generic leaf is homeomorphic to a Cantor tree. Then, we show that all allowed topological types can be simultaneously embedded in the same lamination. This result, together with results of Alvarez-Brum-Mart铆nez-Potrie and Blanc, complete the panorama of understanding which topological surfaces ca… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2005.09050v2-abstract-full').style.display = 'inline'; document.getElementById('2005.09050v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2005.09050v2-abstract-full" style="display: none;"> We give the topological obstructions to be a leaf in a minimal lamination by hyperbolic surfaces whose generic leaf is homeomorphic to a Cantor tree. Then, we show that all allowed topological types can be simultaneously embedded in the same lamination. This result, together with results of Alvarez-Brum-Mart铆nez-Potrie and Blanc, complete the panorama of understanding which topological surfaces can be leaves in minimal hyperbolic surface laminations when the topology of the generic leaf is given. In all cases, all possible topologies can be realized simultaneously. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2005.09050v2-abstract-full').style.display = 'none'; document.getElementById('2005.09050v2-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 February, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 18 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">40 pages. 15 figures. Final version. To appear in Groups, Geometry and Dynamics</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2001.10286">arXiv:2001.10286</a> <span> [<a href="https://arxiv.org/pdf/2001.10286">pdf</a>, <a href="https://arxiv.org/ps/2001.10286">ps</a>, <a href="https://arxiv.org/format/2001.10286">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Group Theory">math.GR</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Metric Geometry">math.MG</span> </div> </div> <p class="title is-5 mathjax"> On the geometry of positive cones in finitely generated groups </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Alonso%2C+J">J. Alonso</a>, <a href="/search/math?searchtype=author&query=Antol%C3%ADn%2C+Y">Y. Antol铆n</a>, <a href="/search/math?searchtype=author&query=Brum%2C+J">J. Brum</a>, <a href="/search/math?searchtype=author&query=Rivas%2C+C">C. Rivas</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="2001.10286v2-abstract-short" style="display: inline;"> We study the geometry of positive cones of left-invariant total orders (left-order, for short) in finitely generated groups. We introduce the \textit{Hucha property} and the \texit{Prieto property} for left-orderable groups. The first one means that in any left-order the corresponding positive cone is not coarsely connected, and the second one that in any left-order the corresponding positive cone… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2001.10286v2-abstract-full').style.display = 'inline'; document.getElementById('2001.10286v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2001.10286v2-abstract-full" style="display: none;"> We study the geometry of positive cones of left-invariant total orders (left-order, for short) in finitely generated groups. We introduce the \textit{Hucha property} and the \texit{Prieto property} for left-orderable groups. The first one means that in any left-order the corresponding positive cone is not coarsely connected, and the second one that in any left-order the corresponding positive cone is coarsely connected. We show that all left-orderable free products have the Hucha property, and that the Hucha property is stable under certain free products with amalgamatation over Prieto subgroups. As an application we show that non-abelian limit groups in the sense of Z. Sela (e.g. free groups, fundamental group of hyperbolic surfaces, doubles of free groups and others) and non-abelian finitely generated subgroups of free $\mathbb{Q}$-groups in the sense of G. Baumslag have the Hucha property. In particular, this implies that these groups have empty BNS-invariant $危^1$ and that they don't have finitely generated positive cones. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2001.10286v2-abstract-full').style.display = 'none'; document.getElementById('2001.10286v2-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 January, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 28 January, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 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">32 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 20F60; 20E08; 20F67 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1906.10029">arXiv:1906.10029</a> <span> [<a href="https://arxiv.org/pdf/1906.10029">pdf</a>, <a href="https://arxiv.org/format/1906.10029">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"> Topology of leaves for minimal laminations by hyperbolic surfaces </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Alvarez%2C+S">S茅bastien Alvarez</a>, <a href="/search/math?searchtype=author&query=Brum%2C+J">Joaqu铆n Brum</a>, <a href="/search/math?searchtype=author&query=Mart%C3%ADnez%2C+M">Matilde Mart铆nez</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="1906.10029v2-abstract-short" style="display: inline;"> We construct minimal laminations by hyperbolic surfaces whose generic leaf is a disk and contain any prescribed family of surfaces and with a precise control of the topologies of the surfaces that appear. The laminations are constructed via towers of finite coverings of surfaces for which we need to develop a relative version of residual finiteness which may be of independent interest. The main st… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1906.10029v2-abstract-full').style.display = 'inline'; document.getElementById('1906.10029v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1906.10029v2-abstract-full" style="display: none;"> We construct minimal laminations by hyperbolic surfaces whose generic leaf is a disk and contain any prescribed family of surfaces and with a precise control of the topologies of the surfaces that appear. The laminations are constructed via towers of finite coverings of surfaces for which we need to develop a relative version of residual finiteness which may be of independent interest. The main step in establishing this relative version of residual finiteness is to obtain finite covers with control on the \emph{second systole} of the surface, which is done in the appendix. In a companion paper, the case of other generic leaves is treated. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1906.10029v2-abstract-full').style.display = 'none'; document.getElementById('1906.10029v2-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 February, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 24 June, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 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">With an appendix by the authors and Maxime Wolff. 43 pages. 11 figures. Final version. To appear in Journal of Topology</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1712.00066">arXiv:1712.00066</a> <span> [<a href="https://arxiv.org/pdf/1712.00066">pdf</a>, <a href="https://arxiv.org/format/1712.00066">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Group Theory">math.GR</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="Representation Theory">math.RT</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.2018.18.4161">10.2140/agt.2018.18.4161 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Spaces of orders of some one-relator groups </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Alonso%2C+J">Juan Alonso</a>, <a href="/search/math?searchtype=author&query=Brum%2C+J">Joaquin Brum</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="1712.00066v2-abstract-short" style="display: inline;"> We show that certain orderable groups admit no isolated left orders. The groups we consider are cyclic amalgamations of a free group with a general orderable group, the HNN extensions of free groups over cyclic subgroups, and a particular class of one-relator groups. In order to prove the results about orders, we develop perturbation techniques for actions of these groups on the line. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1712.00066v2-abstract-full" style="display: none;"> We show that certain orderable groups admit no isolated left orders. The groups we consider are cyclic amalgamations of a free group with a general orderable group, the HNN extensions of free groups over cyclic subgroups, and a particular class of one-relator groups. In order to prove the results about orders, we develop perturbation techniques for actions of these groups on the line. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1712.00066v2-abstract-full').style.display = 'none'; document.getElementById('1712.00066v2-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 June, 2018; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 30 November, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2017. </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, 6 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 06F15; 20F16 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Algebr. Geom. Topol. 18 (2018) 4161-4185 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1609.09452">arXiv:1609.09452</a> <span> [<a href="https://arxiv.org/pdf/1609.09452">pdf</a>, <a href="https://arxiv.org/ps/1609.09452">ps</a>, <a href="https://arxiv.org/format/1609.09452">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="Group Theory">math.GR</span> </div> </div> <p class="title is-5 mathjax"> Free orbits for minimal actions on the circle </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Brum%2C+J">Joaqu铆n Brum</a>, <a href="/search/math?searchtype=author&query=Mart%C3%ADnez%2C+M">Matilde Mart铆nez</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="1609.09452v1-abstract-short" style="display: inline;"> We prove that if $螕$ is a countable group without a subgroup isomorphic to $\mathbb{Z}^2$ that acts faithfully and minimally by orientation preserving homeomorphisms on the circle, then it has a free orbit. We give examples showing that this does not hold for actions by homeomorphisms of the line. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1609.09452v1-abstract-full" style="display: none;"> We prove that if $螕$ is a countable group without a subgroup isomorphic to $\mathbb{Z}^2$ that acts faithfully and minimally by orientation preserving homeomorphisms on the circle, then it has a free orbit. We give examples showing that this does not hold for actions by homeomorphisms of the line. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1609.09452v1-abstract-full').style.display = 'none'; document.getElementById('1609.09452v1-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 September, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2016. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1605.07671">arXiv:1605.07671</a> <span> [<a href="https://arxiv.org/pdf/1605.07671">pdf</a>, <a href="https://arxiv.org/ps/1605.07671">ps</a>, <a href="https://arxiv.org/format/1605.07671">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Group Theory">math.GR</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="Representation Theory">math.RT</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/jlms.12044">10.1112/jlms.12044 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Orderings and flexibility of some subgroups of $Homeo_+(\mathbb{R})$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Alonso%2C+J">Juan Alonso</a>, <a href="/search/math?searchtype=author&query=Brum%2C+J">Joaquin Brum</a>, <a href="/search/math?searchtype=author&query=Rivas%2C+C">Crist贸bal Rivas</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="1605.07671v3-abstract-short" style="display: inline;"> In this work we exhibit flexibility phenomena for some (countable) groups acting by order preserving homeomorphisms of the line. More precisely, we show that if a left orderable group admits an amalgam decomposition of the form $G=\mathbb{F}_n*_{\mathbb Z} \mathbb{F}_m$ where $n+m\geq 3$, then every faithful action of $G$ on the line by order preserving homeomorphisms can be approximated by anothe… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1605.07671v3-abstract-full').style.display = 'inline'; document.getElementById('1605.07671v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1605.07671v3-abstract-full" style="display: none;"> In this work we exhibit flexibility phenomena for some (countable) groups acting by order preserving homeomorphisms of the line. More precisely, we show that if a left orderable group admits an amalgam decomposition of the form $G=\mathbb{F}_n*_{\mathbb Z} \mathbb{F}_m$ where $n+m\geq 3$, then every faithful action of $G$ on the line by order preserving homeomorphisms can be approximated by another action (without global fixed points) that is not semi-conjugated to the initial action. We deduce that $\mathcal{LO}(G)$, the space of left orders of $G$, is a Cantor set. In the special case where $G=蟺_1(危)$ is the fundamental group of a closed hyperbolic surface, we found finer techniques of perturbation. For instance, we exhibit a single representation whose conjugacy class in dense in the space of representations. This entails that the space of representations without global fixed points of $蟺_1(危)$ into $Homeo_+(\mathbb R)$ is connected, and also that the natural conjugation action of $蟺_1(危)$ on $\mathcal{LO}(蟺_1(危))$ has a dense orbit. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1605.07671v3-abstract-full').style.display = 'none'; document.getElementById('1605.07671v3-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 July, 2017; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 24 May, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 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">27 pages, theorem about amalgams added</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 06F15; 20F16 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Journal Lond. Math. Soc. 95 (2017) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/0805.1493">arXiv:0805.1493</a> <span> [<a href="https://arxiv.org/pdf/0805.1493">pdf</a>, <a href="https://arxiv.org/ps/0805.1493">ps</a>, <a href="https://arxiv.org/format/0805.1493">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"> Local product structure for expansive homeomorphisms </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Artigue%2C+A">Alfonso Artigue</a>, <a href="/search/math?searchtype=author&query=Brum%2C+J">Joaquin Brum</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="0805.1493v2-abstract-short" style="display: inline;"> Let $f\colon M\to M$ be an expansive homeomorphism with dense topologically hyperbolic periodic points, $M$ a compact manifold. Then there is a local product structure in an open and dense subset of $M$. Moreover, if some topologically hyperbolic periodic point has codimension one, then this local product structure is uniform. In particular, we conclude that the homeomorphism is conjugated to a… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0805.1493v2-abstract-full').style.display = 'inline'; document.getElementById('0805.1493v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="0805.1493v2-abstract-full" style="display: none;"> Let $f\colon M\to M$ be an expansive homeomorphism with dense topologically hyperbolic periodic points, $M$ a compact manifold. Then there is a local product structure in an open and dense subset of $M$. Moreover, if some topologically hyperbolic periodic point has codimension one, then this local product structure is uniform. In particular, we conclude that the homeomorphism is conjugated to a linear Anosov diffeomorphism of a torus. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('0805.1493v2-abstract-full').style.display = 'none'; document.getElementById('0805.1493v2-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 November, 2008; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 10 May, 2008; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 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">19 pages, Some corrections made</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 37B99; 37D45; 54H20 </p> </li> </ol> <div 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