4 citations · 8 across the 4 of their papers we have counts for
6 papers
Cheeger constant and algebraic entropy of linear groups
Emmanuel Breuillard, Tsachik Gelander
We prove a uniform version of the Tits alternative. As a consequence, we obtain uniform lower bounds for the Cheeger constant of Cayley grahs of finitely generated non virtually so…
Countable Primitive Groups
Tsachik Gelander, Yair Glasner
We give a complete characterization of countable primitive groups in several settings including linear groups, subgroups of mapping class groups, groups acting minimally on trees a…
A topological Tits alternative
Emmanuel Breuillard, Tsachik Gelander
Let k be a local field, and G a linear group over k. We prove that either G contains a relatively open solvable subgroup, or it contains a relatively dense free subgroup. This resu…
On dense free subgroups of Lie groups
Emmanuel Breuillard, Tsachik Gelander
We give a method for constructing dense and free subgroups in real Lie groups. In particular we show that any dense subgroup of a connected semisimple real Lie group G contains a f…
Non-compact arithmetic manifolds have simple homotopy type
Tsachik Gelander
We formulate a conjecture that arithmetic locally symmetric manifolds have simple homotopy type, and prove it for the non-compact case. More precisely, we show that, for any symmet…
Homotopy type and volume of locally symmetric manifolds
Tsachik Gelander
We consider locally symmetric manifolds with a fixed universal covering, and construct for each such manifold M a simplicial complex R whose size is proportional to the volume of M…