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Simply transitive geodesics and omnipotence of lattices in PSL$(2,mathbb{C})$ PSL$(2,mathbb{C})$中的简单传递测地线和网格全能性
arXiv - MATH - Group Theory Pub Date : 2024-09-12 DOI: arxiv-2409.08418
Ian Agol, Tam Cheetham-West, Yair Minsky
{"title":"Simply transitive geodesics and omnipotence of lattices in PSL$(2,mathbb{C})$","authors":"Ian Agol, Tam Cheetham-West, Yair Minsky","doi":"arxiv-2409.08418","DOIUrl":"https://doi.org/arxiv-2409.08418","url":null,"abstract":"We show that the isometry group of a finite-volume hyperbolic 3-manifold acts\u0000simply transitively on many of its closed geodesics. Combining this observation\u0000with the Virtual Special Theorems of the first author and Wise, we show that\u0000every non-arithmetic lattice in PSL$(2,mathbb{C})$ is the full group of\u0000orientation-preserving isometries for some other lattice and that the\u0000orientation-preserving isometry group of a finite-volume hyperbolic 3-manifold\u0000acts non-trivially on the homology of some finite-sheeted cover.","PeriodicalId":501037,"journal":{"name":"arXiv - MATH - Group Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142253761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Special Moufang sets of finite dimension 有限维度的特殊毛方集
arXiv - MATH - Group Theory Pub Date : 2024-09-11 DOI: arxiv-2409.07445
Matthias Grüninger
{"title":"Special Moufang sets of finite dimension","authors":"Matthias Grüninger","doi":"arxiv-2409.07445","DOIUrl":"https://doi.org/arxiv-2409.07445","url":null,"abstract":"We prove that a special Moufang sets with abelian root subgroups derive from\u0000a quadratic Jordan division algebra if a certain finiteness condition is\u0000satisfied.","PeriodicalId":501037,"journal":{"name":"arXiv - MATH - Group Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Conjugacy classes of completely reducible cyclic subgroups of GL$(2, q)$ GL$(2, q)$ 的完全还原循环子群的共轭类
arXiv - MATH - Group Theory Pub Date : 2024-09-11 DOI: arxiv-2409.07244
Prashun Kumar, Geetha Venkataraman
{"title":"Conjugacy classes of completely reducible cyclic subgroups of GL$(2, q)$","authors":"Prashun Kumar, Geetha Venkataraman","doi":"arxiv-2409.07244","DOIUrl":"https://doi.org/arxiv-2409.07244","url":null,"abstract":"Let $m$ be a positive integer such that $p$ does not divide $m$ where $p$ is\u0000prime. In this paper we find the number of conjugacy classes of completely\u0000reducible cyclic subgroups in GL$(2, q)$ of order $m$, where $q$ is a power of\u0000$p$.","PeriodicalId":501037,"journal":{"name":"arXiv - MATH - Group Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
$mathcal{C}$-Hereditarily conjugacy separable groups and wreath products $mathcal{C}$氦共轭可分离群和花环积
arXiv - MATH - Group Theory Pub Date : 2024-09-10 DOI: arxiv-2409.06200
Alexander Bishop, Michal Ferov, Mark Pengitore
{"title":"$mathcal{C}$-Hereditarily conjugacy separable groups and wreath products","authors":"Alexander Bishop, Michal Ferov, Mark Pengitore","doi":"arxiv-2409.06200","DOIUrl":"https://doi.org/arxiv-2409.06200","url":null,"abstract":"We provide a necessary and sufficient condition for the restricted wreath\u0000product $Awr B$ to be $mathcal{C}$-hereditarily conjugacy separable where\u0000$mathcal{C}$ is an extension-closed pseudo-variety of finite groups. Moreover,\u0000we prove that the Grigorchuk group is 2-hereditarily conjugacy separable.","PeriodicalId":501037,"journal":{"name":"arXiv - MATH - Group Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generating Extended Mapping Class Groups with Two Periodic Elements 用两个周期元素生成扩展映射类群
arXiv - MATH - Group Theory Pub Date : 2024-09-10 DOI: arxiv-2409.06350
Reid Harris
{"title":"Generating Extended Mapping Class Groups with Two Periodic Elements","authors":"Reid Harris","doi":"arxiv-2409.06350","DOIUrl":"https://doi.org/arxiv-2409.06350","url":null,"abstract":"The extended mapping class group of a surface $Sigma$ is defined to be the\u0000group of isotopy classes of (not necessarily orientation-preserving)\u0000homeomorphisms of $Sigma$. We are able to show that the extended mapping class\u0000group of an $n$-punctured sphere is generated by two elements of finite order\u0000exactly when $nnot=4$. We use this result to prove that the extended mapping\u0000class group of a genus 2 surface is generated by two elements of finite order.","PeriodicalId":501037,"journal":{"name":"arXiv - MATH - Group Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hierarchical hyperbolicity of admissible curve graphs and the boundary of marked strata 可容许曲线图的层次双曲性和标记层的边界
arXiv - MATH - Group Theory Pub Date : 2024-09-10 DOI: arxiv-2409.06798
Aaron Calderon, Jacob Russell
{"title":"Hierarchical hyperbolicity of admissible curve graphs and the boundary of marked strata","authors":"Aaron Calderon, Jacob Russell","doi":"arxiv-2409.06798","DOIUrl":"https://doi.org/arxiv-2409.06798","url":null,"abstract":"We show that for any surface of genus at least 3 equipped with any choice of\u0000framing, the graph of non-separating curves with winding number 0 with respect\u0000to the framing is hierarchically hyperbolic but not Gromov hyperbolic. We also\u0000describe how to build analogues of the curve graph for marked strata of abelian\u0000differentials that capture the combinatorics of their boundaries, analogous to\u0000how the curve graph captures the combinatorics of the augmented Teichmueller\u0000space. These curve graph analogues are also shown to be hierarchically, but not\u0000Gromov, hyperbolic.","PeriodicalId":501037,"journal":{"name":"arXiv - MATH - Group Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Positivity, cross-ratios and the Collar Lemma 正向性、交叉比和项圈定理
arXiv - MATH - Group Theory Pub Date : 2024-09-10 DOI: arxiv-2409.06294
Jonas BeyrerUNISTRA, Olivier GuichardUNISTRA, François LabourieUniCA, Beatrice Pozzetti, Anna Wienhard
{"title":"Positivity, cross-ratios and the Collar Lemma","authors":"Jonas BeyrerUNISTRA, Olivier GuichardUNISTRA, François LabourieUniCA, Beatrice Pozzetti, Anna Wienhard","doi":"arxiv-2409.06294","DOIUrl":"https://doi.org/arxiv-2409.06294","url":null,"abstract":"We prove that $Theta$-positive representations of fundamental groups of\u0000surfaces (possibly cusped or of infinite type) satisfy a collar lemma, and\u0000their associated cross-ratios are positive. As a consequence we deduce that\u0000$Theta$-positive representations form closed subsets of the representation\u0000variety.","PeriodicalId":501037,"journal":{"name":"arXiv - MATH - Group Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On semitopological simple inverse $ω$-semigroups with compact maximal subgroups 论具有紧凑最大子群的半拓扑简单逆ω$半群
arXiv - MATH - Group Theory Pub Date : 2024-09-10 DOI: arxiv-2409.06344
Oleg Gutik, Kateryna Maksymyk
{"title":"On semitopological simple inverse $ω$-semigroups with compact maximal subgroups","authors":"Oleg Gutik, Kateryna Maksymyk","doi":"arxiv-2409.06344","DOIUrl":"https://doi.org/arxiv-2409.06344","url":null,"abstract":"We describe the structure of simple inverse Hausdorff semitopological\u0000$omega$-semigroups with compact maximal subgroups. In particular we show that\u0000if $S$ is a simple inverse Hausdorff semitopological $omega$-semigroups with\u0000compact maximal subgroups, then $S$ is topologically isomorphic to the\u0000Bruck--Reilly extension\u0000$left(textbf{BR}(T,theta),tau_{textbf{BR}}^{oplus}right)$ of a finite\u0000semilattice $T=left[E;G_alpha,varphi_{alpha,beta}right]$ of compact\u0000groups $G_alpha$ in the class of topological inverse semigroups, where\u0000$tau_{textbf{BR}}^{oplus}$ is the sum direct topology on\u0000$textbf{BR}(T,theta)$. Also we prove that every Hausdorff locally compact\u0000shift-continuous topology on the simple inverse Hausdorff semitopological\u0000$omega$-semigroups with compact maximal subgroups with adjoined zero is either\u0000compact or discrete.","PeriodicalId":501037,"journal":{"name":"arXiv - MATH - Group Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Presentation of kernels of rational characters of right-angled Artin groups 直角阿尔丁群有理特征的内核表述
arXiv - MATH - Group Theory Pub Date : 2024-09-10 DOI: arxiv-2409.06315
Montserrat Casals-Ruiz, Ilya Kazachkov, Mallika Roy
{"title":"Presentation of kernels of rational characters of right-angled Artin groups","authors":"Montserrat Casals-Ruiz, Ilya Kazachkov, Mallika Roy","doi":"arxiv-2409.06315","DOIUrl":"https://doi.org/arxiv-2409.06315","url":null,"abstract":"In this note, we characterise when the kernel of a rational character of a\u0000right-anlged Artin group, also known as generalised Bestiva-Brady group, is\u0000finitely generated and finitely presented. In these cases, we exhibit a finite\u0000generating set and a presentation. These results generalise Dicks and Leary's\u0000presentations of Bestina-Brady kernels and provide an algebraic proof for the\u0000results proven by Meier, Meinert, and VanWyk.","PeriodicalId":501037,"journal":{"name":"arXiv - MATH - Group Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Out($F_r$) train track automata I: Proper full fold decompositions Out($F_r$) 火车轨道自动机 I：适当的全折分解
arXiv - MATH - Group Theory Pub Date : 2024-09-09 DOI: arxiv-2409.05599
Catherine Eva Pfaff
{"title":"Out($F_r$) train track automata I: Proper full fold decompositions","authors":"Catherine Eva Pfaff","doi":"arxiv-2409.05599","DOIUrl":"https://doi.org/arxiv-2409.05599","url":null,"abstract":"We describe train track automata for large classes of fully irreducible\u0000elements of Out($F_r$), and their associated geodesics in Culler-Vogtmann Outer\u0000Space.","PeriodicalId":501037,"journal":{"name":"arXiv - MATH - Group Theory","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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