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Realizing invariant random subgroups as stabilizer distributions 实现不变随机子群作为稳定分布
3区 数学
Groups Geometry and Dynamics Pub Date : 2023-11-11 DOI: 10.4171/ggd/757
Simon Thomas
{"title":"Realizing invariant random subgroups as stabilizer distributions","authors":"Simon Thomas","doi":"10.4171/ggd/757","DOIUrl":"https://doi.org/10.4171/ggd/757","url":null,"abstract":". Suppose that ν is an ergodic IRS of a countable group G such that [ N G ( H ) : H ] = n < ∞ for ν -a.e. H ∈ Sub G . In this paper, we consider the question of whether ν can be realized as the stabilizer distribution of an ergodic action G ↷ ( X,µ ) on a standard Borel probability space such that the stabilizer map x (cid:55)→ G x is n -to-one.","PeriodicalId":55084,"journal":{"name":"Groups Geometry and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135042423","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
Group boundaries for semidirect products with $mathbb{Z}$ $mathbb{Z}$的半直积的群边界
3区 数学
Groups Geometry and Dynamics Pub Date : 2023-11-09 DOI: 10.4171/ggd/750
Craig R. Guilbault, Brendan Burns Healy, Brian Pietsch
{"title":"Group boundaries for semidirect products with $mathbb{Z}$","authors":"Craig R. Guilbault, Brendan Burns Healy, Brian Pietsch","doi":"10.4171/ggd/750","DOIUrl":"https://doi.org/10.4171/ggd/750","url":null,"abstract":"","PeriodicalId":55084,"journal":{"name":"Groups Geometry and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135192979","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
Symbolic group varieties and dual surjunctivity 符号群变异与对偶上通性
3区 数学
Groups Geometry and Dynamics Pub Date : 2023-11-08 DOI: 10.4171/ggd/749
Xuan Kien Phung
{"title":"Symbolic group varieties and dual surjunctivity","authors":"Xuan Kien Phung","doi":"10.4171/ggd/749","DOIUrl":"https://doi.org/10.4171/ggd/749","url":null,"abstract":"Let $G$ be a group. Let $X$ be an algebraic group over an algebraically closed field $K$. Denote by $A=X(K)$ the set of rational points of $X$. We study algebraic group cellular automata $tau colon A^G to A^G$ whose local defining map is induced by a homomorphism of algebraic groups $X^M to X$ where $M$ is a finite memory. When $G$ is sofic and $K$ is uncountable, we show that if $tau$ is post-surjective then it is weakly pre-injective. Our result extends the dual version of Gottschalk's Conjecture for finite alphabets proposed by Capobianco, Kari, and Taati. When $G$ is amenable, we prove that if $tau$ is surjective then it is weakly pre-injective, and conversely, if $tau$ is pre-injective then it is surjective. Hence, we obtain a complete answer to a question of Gromov on the Garden of Eden theorem in the case of algebraic group cellular automata.","PeriodicalId":55084,"journal":{"name":"Groups Geometry and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135292799","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
Constructing pseudo-Anosovs from expanding interval maps 从展开区间映射构造伪anosov
3区 数学
Groups Geometry and Dynamics Pub Date : 2023-11-07 DOI: 10.4171/ggd/745
Ethan Farber
{"title":"Constructing pseudo-Anosovs from expanding interval maps","authors":"Ethan Farber","doi":"10.4171/ggd/745","DOIUrl":"https://doi.org/10.4171/ggd/745","url":null,"abstract":"We investigate a phenomenon observed by W. Thurston wherein one constructs a pseudo-Anosov homeomorphism on the limit set of a certain lift of a piecewise-linear expanding interval map. We reconcile this construction with a special subclass of generalized pseudo-Anosovs, first defined by de Carvalho. From there we classify the circumstances under which this construction produces a pseudo-Anosov. As an application, we produce for each $g geq 1$ a pseudo-Anosov $phi_g$ on the surface of genus $g$ that preserves an algebraically primitive translation structure and whose dilatation $lambda_g$ is a Salem number.","PeriodicalId":55084,"journal":{"name":"Groups Geometry and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135431079","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
Groups with minimal harmonic functions as small as you like (with an appendix by Nicolás Matte Bon) 具有最小调和函数的群，只要你喜欢(附Nicolás Matte Bon的附录)
3区 数学
Groups Geometry and Dynamics Pub Date : 2023-11-04 DOI: 10.4171/ggd/748
Gideon Amir, Gady Kozma
{"title":"Groups with minimal harmonic functions as small as you like (with an appendix by Nicolás Matte Bon)","authors":"Gideon Amir, Gady Kozma","doi":"10.4171/ggd/748","DOIUrl":"https://doi.org/10.4171/ggd/748","url":null,"abstract":"For any order of growth $f(n)=o(log n)$ we construct a finitely-generated group $G$ and a set of generators $S$ such that the Cayley graph of $G$ with respect to $S$ supports a harmonic function with growth $f$ but does not support any harmonic function with slower growth. The construction uses permutational wreath products in which the base group is defined via its properly chosen Schreier graph.","PeriodicalId":55084,"journal":{"name":"Groups Geometry and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135726750","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
Exponent of self-similar finite $p$-groups 自相似有限群的指数
3区 数学
Groups Geometry and Dynamics Pub Date : 2023-10-30 DOI: 10.4171/ggd/754
Alex Carrazedo Dantas, Emerson de Melo
{"title":"Exponent of self-similar finite $p$-groups","authors":"Alex Carrazedo Dantas, Emerson de Melo","doi":"10.4171/ggd/754","DOIUrl":"https://doi.org/10.4171/ggd/754","url":null,"abstract":"Let $p$ be a prime and $G$ a pro-$p$ group of finite rank that admits a faithful, self-similar action on the $p$-ary rooted tree. We prove that if the set ${gin G | g^{p^n}=1}$ is a nontrivial subgroup for some $n$, then $G$ is a finite $p$-group with exponent at most $p^n$. This applies in particular to power abelian $p$-groups.","PeriodicalId":55084,"journal":{"name":"Groups Geometry and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136018112","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
Splittings of triangle Artin groups 三角形Artin群体的分裂
3区 数学
Groups Geometry and Dynamics Pub Date : 2023-10-15 DOI: 10.4171/ggd/740
Kasia Jankiewicz
{"title":"Splittings of triangle Artin groups","authors":"Kasia Jankiewicz","doi":"10.4171/ggd/740","DOIUrl":"https://doi.org/10.4171/ggd/740","url":null,"abstract":"We show that a triangle Artin group $mathrm{Art}_{MNP}$, where $Mleq Nleq P$, splits as an amalgamated product or an HNN extension of finite rank free groups, provided that either $M>2$ or $N>3$. We also prove that all even 3-generator Artin groups are residually finite.","PeriodicalId":55084,"journal":{"name":"Groups Geometry and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136183496","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
Tight inclusions of $C^*$-dynamical systems $C^*$-动力系统的紧密内含
3区 数学
Groups Geometry and Dynamics Pub Date : 2023-10-14 DOI: 10.4171/ggd/739
Yair Hartman, Mehrdad Kalantar
{"title":"Tight inclusions of $C^*$-dynamical systems","authors":"Yair Hartman, Mehrdad Kalantar","doi":"10.4171/ggd/739","DOIUrl":"https://doi.org/10.4171/ggd/739","url":null,"abstract":"We study a notion of tight inclusions of $C^$- and $W^$-dynamical systems, which is meant to capture a tension between topological and measurable rigidity of boundary actions. An important case of such inclusions is $C(X)subset L^infty(X, nu)$ for measurable boundaries with unique stationary compact models. We discuss the implications of this phenomenon in the description of Zimmer amenable intermediate factors. Furthermore, we prove applications in the problem of maximal injectivity of von Neumann algebras.","PeriodicalId":55084,"journal":{"name":"Groups Geometry and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135765929","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
On the continuity of the growth rate on the space of Coxeter systems 关于Coxeter系统空间上增长率的连续性
3区 数学
Groups Geometry and Dynamics Pub Date : 2023-10-08 DOI: 10.4171/ggd/741
Tomoshige Yukita
{"title":"On the continuity of the growth rate on the space of Coxeter systems","authors":"Tomoshige Yukita","doi":"10.4171/ggd/741","DOIUrl":"https://doi.org/10.4171/ggd/741","url":null,"abstract":"Floyd showed that if a sequence of compact hyperbolic Coxeter polygons converges, then so does the sequence of the growth rates of the Coxeter groups associated with the polygons. For the case of the hyperbolic 3-space, Kolpakov discovered the same phenomena for specific convergent sequences of hyperbolic Coxeter polyhedra. In this paper, we show that the growth rate is a continuous function on the space of Coxeter systems. This is an extension of the results due to Floyd and Kolpakov since the convergent sequences of Coxeter polyhedra give rise to that of Coxeter systems in the space of marked groups.","PeriodicalId":55084,"journal":{"name":"Groups Geometry and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135197669","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
Globally stable cylinders for hyperbolic CAT(0) cube complexes 双曲CAT(0)立方配合物的全局稳定柱体
3区 数学
Groups Geometry and Dynamics Pub Date : 2023-10-06 DOI: 10.4171/ggd/744
Nir Lazarovich, Michah Sageev
{"title":"Globally stable cylinders for hyperbolic CAT(0) cube complexes","authors":"Nir Lazarovich, Michah Sageev","doi":"10.4171/ggd/744","DOIUrl":"https://doi.org/10.4171/ggd/744","url":null,"abstract":"Rips and Sela introduced the notion of globally stable cylinders and asked if all Gromov hyperbolic groups admit such. We prove that hyperbolic cubulated groups admit globally stable cylinders.","PeriodicalId":55084,"journal":{"name":"Groups Geometry and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135302595","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
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