Zobrazeno 1 - 10
of 71
pro vyhledávání: '"Gaboriau, Damien"'
We continue our study of the perfect kernel of the space of transitive actions of Baumslag-Solitar groups by investigating high transitivity. We show that actions of finite phenotype are never highly transitive, except when the phenotype is $1$, in w
Externí odkaz:
http://arxiv.org/abs/2410.23224
Autor:
Azuelos, Pénélope, Gaboriau, Damien
We introduce several approaches to studying the Cantor-Bendixson decomposition of and the dynamics on the (topological) space of subgroups for various families of countable groups. In particular, we uncover the perfect kernel and the Cantor-Bendixson
Externí odkaz:
http://arxiv.org/abs/2308.05954
Given a Baumslag-Solitar group, we study its space of subgroups from a topological and dynamical perspective. We first determine its perfect kernel (the largest closed subset without isolated points). We then bring to light a natural partition of the
Externí odkaz:
http://arxiv.org/abs/2210.14990
Let $n\ge 3$, and let $\mathrm{Out}(W_n)$ be the outer automorphism group of a free Coxeter group $W_n$ of rank $n$. We study the growth of the dimension of the homology groups (with coefficients in any field $\mathbb{K}$) along Farber sequences of f
Externí odkaz:
http://arxiv.org/abs/2209.02760
We prove new vanishing results on the growth of higher torsion homologies for suitable arithmetic lattices, Artin groups and mapping class groups. The growth is understood along Farber sequences, in particular, along residual chains. For principal co
Externí odkaz:
http://arxiv.org/abs/2106.13051
We show that several new classes of groups are measure strongly treeable. In particular, finitely generated groups admitting planar Cayley graphs, elementarily free groups, and the group of isometries of the hyperbolic plane and all its closed subgro
Externí odkaz:
http://arxiv.org/abs/2104.07431
Publikováno v:
Geom. Topol. 27 (2023) 2297-2318
We study probability measure preserving (p.m.p.) non-free actions of free groups and the associated IRS's. The perfect kernel of a countable group Gamma is the largest closed subspace of the space of subgroups of Gamma without isolated points. We int
Externí odkaz:
http://arxiv.org/abs/2009.03080
Autor:
Gaboriau, Damien, Noûs, Camille
Publikováno v:
Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques, Serie 6, Volume 30 (2021) no. 5, pp. 1121-1137
The purpose of this note is to introduce a trick which relates the (non)-vanishing of the top-dimensional $\ell^2$-Betti numbers of actions with that of sub-actions. We provide three different types of applications: we prove that the $\ell^2$-Betti n
Externí odkaz:
http://arxiv.org/abs/1909.01633
Publikováno v:
Annales Henri Lebesgue, Volume 4 (2021), pp. 1235-1293
We consider probability measure preserving discrete groupoids, group actions and equivalence relations in the context of general probability spaces. We study for these objects the notions of cost, $\beta$-invariant and some higher-dimensional variant
Externí odkaz:
http://arxiv.org/abs/1812.00704
Autor:
Gaboriau, Damien
The entropy in dynamical systems was introduced by A. Kolmogorov. Initially dedicated to iterations of one finite measure preserving transformation, the notion was gradually generalized so as to encompass amenable group actions and topological action
Externí odkaz:
http://arxiv.org/abs/1607.06454