4 papers
Topology and dynamics of unimodular random hyperbolic manifolds
Ilya Gekhtman, Nir Lazarovich, Arie Levit +1
We investigate the relationship between the space of ends of a unimodular random hyperbolic manifold and the dynamics of its geodesic flow. We show that having two ends of infinite…
Stationary random subgroups in negative curvature
Ilya Gekhtman, Arie Levit
We show that discrete stationary random subgroups of isometry groups of Gromov hyperbolic spaces have full limit sets as well as critical exponents bounded from below. This informa…
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…
Surface groups are flexibly stable
Nir Lazarovich, Arie Levit, Yair Minsky
We show that surface groups are flexibly stable in permutations. This is the first non-trivial example of a non-amenable flexibly stable group. Our method is purely geometric and r…