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On topological full groups of $mathbb Z^d$-actions 关于$mathbb Z^d$-动作的拓扑满群
IF 0.6 3区 数学
Groups Geometry and Dynamics Pub Date : 2020-02-27 DOI: 10.4171/ggd/534
M. Chornyi, K. Juschenko, V. Nekrashevych
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引用次数: 0
Conjugacy and centralizers in groups of piecewise projective homeomorphisms 分段投影同胚群中的共轭性与中心子
IF 0.6 3区 数学
Groups Geometry and Dynamics Pub Date : 2020-02-25 DOI: 10.4171/ggd/657
Francesco Matucci, Altair Santos de Oliveira-Tosti
{"title":"Conjugacy and centralizers in groups of piecewise projective homeomorphisms","authors":"Francesco Matucci, Altair Santos de Oliveira-Tosti","doi":"10.4171/ggd/657","DOIUrl":"https://doi.org/10.4171/ggd/657","url":null,"abstract":"Monod introduced in [14] a family of Thompson-like groups which provides natural counterexamples to the von Neumann-Day conjecture. We construct a characterization of conjugacy and invariant and use them to compute centralizers in one group of this family.","PeriodicalId":55084,"journal":{"name":"Groups Geometry and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48841154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Comparison theorems for closed geodesics on negatively curved surfaces 负曲面上封闭测地线的比较定理
IF 0.6 3区 数学
Groups Geometry and Dynamics Pub Date : 2020-02-22 DOI: 10.4171/ggd/671
S. Cantrell, M. Pollicott
{"title":"Comparison theorems for closed geodesics on negatively curved surfaces","authors":"S. Cantrell, M. Pollicott","doi":"10.4171/ggd/671","DOIUrl":"https://doi.org/10.4171/ggd/671","url":null,"abstract":"In this note we present new asymptotic estimates comparing the word length and geodesic length of closed geodesics on surfaces with (variable) negative sectional curvatures. In particular, we provide an averaged comparison of these two important quantities and obtain precise statistical results, including a central limit theorem and a local limit theorem. Further, as a corollary we also improve an asymptotic formula of R. Sharp and the second author. Finally, we relate our results to recent work of Gekhtman, Taylor and Tiozzo.","PeriodicalId":55084,"journal":{"name":"Groups Geometry and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41983272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Characters of algebraic groups over number fields 数域上代数群的特征
IF 0.6 3区 数学
Groups Geometry and Dynamics Pub Date : 2020-02-18 DOI: 10.4171/ggd/678
Bachir Bekka, Camille Francini
{"title":"Characters of algebraic groups over number fields","authors":"Bachir Bekka, Camille Francini","doi":"10.4171/ggd/678","DOIUrl":"https://doi.org/10.4171/ggd/678","url":null,"abstract":"Let k be a number field, G an algebraic group defined over k, and G(k) the group of k-rational points in G. We determine the set of functions on G(k) which are of positive type and conjugation invariant, under the assumption that G(k) is generated by its unipotent elements. An essential step in the proof is the classification of the G(k)-invariant ergodic probability measures on an adelic solenoid naturally associated to G(k); this last result is deduced from Ratner's measure rigidity theorem for homogeneous spaces of S-adic Lie groups.","PeriodicalId":55084,"journal":{"name":"Groups Geometry and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48169315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
The automorphism group of Rauzy diagrams Rauzy图的同构群
IF 0.6 3区 数学
Groups Geometry and Dynamics Pub Date : 2020-02-17 DOI: 10.4171/ggd/728
Corentin Boissy
{"title":"The automorphism group of Rauzy diagrams","authors":"Corentin Boissy","doi":"10.4171/ggd/728","DOIUrl":"https://doi.org/10.4171/ggd/728","url":null,"abstract":"We give a description of the automorphism group of a Rauzy diagram as a subgroup of the symmetric group. This is based on an example that appear in some personnal notes of Yoccoz that are to be published in the project ''Yoccoz archives''.","PeriodicalId":55084,"journal":{"name":"Groups Geometry and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47133199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Divergence of finitely presented groups 有限表示群的散度
IF 0.6 3区 数学
Groups Geometry and Dynamics Pub Date : 2020-02-10 DOI: 10.4171/ggd/632
N. Brady, H. Tran
{"title":"Divergence of finitely presented groups","authors":"N. Brady, H. Tran","doi":"10.4171/ggd/632","DOIUrl":"https://doi.org/10.4171/ggd/632","url":null,"abstract":"We construct families of finitely presented groups exhibiting new divergence behavior; we obtain divergence functions of the form $r^alpha$ for a dense set of exponents $alpha in [2,infty)$ and $r^nlog(r)$ for integers $n geq 2$. The same construction also yields examples of finitely presented groups which contain Morse elements that are not contracting.","PeriodicalId":55084,"journal":{"name":"Groups Geometry and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44106456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
On hereditarily self-similar $p$-adic analytic pro-$p$ groups 关于遗传自相似$p$adic分析pro-$p$群
IF 0.6 3区 数学
Groups Geometry and Dynamics Pub Date : 2020-02-06 DOI: 10.4171/ggd/641
Francesco Noseda, I. Snopce
{"title":"On hereditarily self-similar $p$-adic analytic pro-$p$ groups","authors":"Francesco Noseda, I. Snopce","doi":"10.4171/ggd/641","DOIUrl":"https://doi.org/10.4171/ggd/641","url":null,"abstract":"A non-trivial finitely generated pro-$p$ group $G$ is said to be strongly hereditarily self-similar of index $p$ if every non-trivial finitely generated closed subgroup of $G$ admits a faithful self-similar action on a $p$-ary tree. We classify the solvable torsion-free $p$-adic analytic pro-$p$ groups of dimension less than $p$ that are strongly hereditarily self-similar of index $p$. Moreover, we show that a solvable torsion-free $p$-adic analytic pro-$p$ group of dimension less than $p$ is strongly hereditarily self-similar of index $p$ if and only if it is isomorphic to the maximal pro-$p$ Galois group of some field that contains a primitive $p$-th root of unity. As a key step for the proof of the above results, we classify the 3-dimensional solvable torsion-free $p$-adic analytic pro-$p$ groups that admit a faithful self-similar action on a $p$-ary tree, completing the classification of the 3-dimensional torsion-free $p$-adic analytic pro-$p$ groups that admit such actions.","PeriodicalId":55084,"journal":{"name":"Groups Geometry and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44249529","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Cohomology of hyperfinite Borel actions 超有限Borel作用的上同调
IF 0.6 3区 数学
Groups Geometry and Dynamics Pub Date : 2020-01-24 DOI: 10.4171/ggd/633
S. Bezuglyi, S. Sanadhya
{"title":"Cohomology of hyperfinite Borel actions","authors":"S. Bezuglyi, S. Sanadhya","doi":"10.4171/ggd/633","DOIUrl":"https://doi.org/10.4171/ggd/633","url":null,"abstract":"We study cocycles of countable groups $Gamma$ of Borel automorphisms of a standard Borel space $(X, mathcal{B})$ taking values in a locally compact second countable group $G$. We prove that for a hyperfinite group $Gamma$ the subgroup of coboundaries is dense in the group of cocycles. We describe all Borel cocycles of the $2$-odometer and show that any such cocycle is cohomologous to a cocycle with values in a countable dense subgroup $H$ of $G$. We also provide a Borel version of Gottschalk-Hedlund theorem.","PeriodicalId":55084,"journal":{"name":"Groups Geometry and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47753444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Minimality of the action on the universal circle of uniform foliations 均匀叶形万向圆上作用的极小性
IF 0.6 3区 数学
Groups Geometry and Dynamics Pub Date : 2020-01-15 DOI: 10.4171/ggd/637
Sérgio R. Fenley, R. Potrie
{"title":"Minimality of the action on the universal circle of uniform foliations","authors":"Sérgio R. Fenley, R. Potrie","doi":"10.4171/ggd/637","DOIUrl":"https://doi.org/10.4171/ggd/637","url":null,"abstract":"Given a uniform foliation by Gromov hyperbolic leaves on a $3$-manifold, we show that the action of the fundamental group on the universal circle is minimal and transitive on pairs of different points. We also prove two other results: we prove that general uniform Reebless foliations are $mathbb{R}$-covered and we give a new description of the universal circle of $mathbb{R}$-covered foliations with Gromov hyperbolic leaves in terms of the JSJ decomposition of $M$.","PeriodicalId":55084,"journal":{"name":"Groups Geometry and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46892452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Coherence and one-relator products of locally indicable groups 局部可指示群的相干性和单相关积
IF 0.6 3区 数学
Groups Geometry and Dynamics Pub Date : 2020-01-06 DOI: 10.4171/ggd/725
J. Howie, H. Short
{"title":"Coherence and one-relator products of locally indicable groups","authors":"J. Howie, H. Short","doi":"10.4171/ggd/725","DOIUrl":"https://doi.org/10.4171/ggd/725","url":null,"abstract":"We extend several results of Helfer, Wise, Louder and Wilton related to coherence in one-relator groups to the more general setting of one-relator products of locally indicable groups. The methods developed to do so also give rise to a new proof of a theorem of Brodsky.","PeriodicalId":55084,"journal":{"name":"Groups Geometry and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43343792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
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