7 papers · 1 filter
Things we can learn by considering random locally symmetric manifolds
Tsachik Gelander
In recent years various results about locally symmetric manifolds were proven using probabilistic approaches. One of the approaches is to consider random manifolds by associating a…
Spectral gap for products and a strong normal subgroup theorem
Uri Bader, Tsachik Gelander, Arie Levit
We establish a general spectral gap theorem for actions of products of groups which may replace Kazhdan's property (T) in various situations. As a main application, we prove that a…
Bounds on Systoles and Homotopy Complexity
Tsachik Gelander, Paul Vollrath
We give an elementary proof of a weak variant of the homotopy type conjecture from [Gel04]. The proof relies on Belolipetskys estimate on the systole in terms of the volume which i…
Aut(Fn) actions on representation spaces
Tsachik Gelander
J. Wiegold conjectured that if n>2 and G is a finite simple group, then the action of Aut(F_n) on Epi(F_n,G) is transitive. In this note we consider analogous questions where G is…
Infinite Volume and Infinite Injectivity Radius
Mikolaj Fraczyk, Tsachik Gelander
We prove the following conjecture of Margulis. Let be a higher rank simple Lie group and let be a discrete subgroup of infinite covolume. Then, the locally symmetric…
An Invitation to Analytic Group Theory
Tal Cohen, Tsachik Gelander
This book is concerned with analytic approaches of studying groups and their actions. Much attention is devoted to the study of amenability and Kazhdan's property (T), which are pe…