83 citations · 319 across the 28 of their papers we have counts for
35 papers
Commensurating actions and self-similar groups
Nicolás Matte Bon, Volodymyr Nekrashevych, Tianyi Zheng
Commensurating actions govern how a group can act on non-positively curved cube complexes. We obtain a complete picture of them for a class of finitely generated groups acting on r…
Semigroups, groups, and algebras of dynamical origin
Volodymyr Nekrashevych
The paper is an overview of recent results on algebraic structures (semigroups, groupoids, algebras, inverse semigroups, and groups) associated with objects with a rich set of part…
Simplicity of -algebras of contracting self-similar groups
Eusebio Gardella, Volodymyr Nekrashevych, Benjamin Steinberg +1
We show that the -algebra associated by Nekrashevych to a contracting self-similar group is simple if and only if the corresponding complex -algebra is simple. We also i…
Liouville property for groups and conformal dimension
Nicolás Matte Bon, Volodymyr Nekrashevych, Tianyi Zheng
Conformal dimension is a fundamental invariant of metric spaces, particularly suited to the study of self-similar spaces, such as spaces with an expanding self-covering (e.g. Julia…
Self-similar groups and topological dimension
Volodymyr Nekrashevych
We give various characterizations of the covering dimension of the limit space of a contracting self-similar group. In particular, we show that it is equal to the minimal dimension…
Growth of groups with linear Schreier graphs
Laurent Bartholdi, Volodymyr Nekrashevych, Tianyi Zheng
We introduce a new method of proving upper estimates of growth of finitely generated groups and constructing groups of intermediate growth using graphs of their actions. These esti…