83 citations · 319 across the 28 of their papers we have counts for
25 papers · 1 filter
Conformal dimension and self-similar groups
Volodymyr Nekrashevych
We study the Ahlfors-regular conformal dimension of spaces with locally expanding self-covering maps and, more generally, limit spaces of contracting self-similar groups. We show t…
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…
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…
Substitutional subshifts and growth of groups
Volodymyr Nekrashevych
We show how to use symbolic dynamics of Schreier graphs to embed the Grigorchuk group into a simple torsion group of intermediate growth and to construct uncountably many growth ty…