Let M be a non-elementary convex cocompact hyperbolic 3-manifold and δ be the critical exponent of its fundamental group. We prove that a one-dimensional unipotent flow for the frame bundle of M is ergodic for the Burger-Roblin measure if and only if δ > 1.

For a finitely generated discrete group $\Gamma$ acting properly on spin manifold $M$, we formulate new topological obstructions to $\Gamma$-invariant metrics of positive scalar curvature $M$ that take into account the cohomology classifying space $\underline{B}\Gamma$ for proper actions. In cocompact case, this leads natural generalisation Gromov-Lawson's notion higher $\hat{A}$-genera setting...

We consider a cocompact discrete reflection group W of a CAT(0) space X . Then W becomes a Coxeter group. In this paper, we study an analogy between the Davis-Moussong complex Σ(W, S) and the CAT(0) space X , and show several analogous results about the limit set of a parabolic subgroup of the Coxeter group W .

In this note, we prove that an aspherical fully residually free Kähler group is Fuchsian. One instances of this shows that cocompact lattices in PU(1, n) for n > 1 cannot be residually free. The proof uses some recent work of Delzant and Gromov.

A connection between real poles of the growth functions for Coxeter groups acting on hyperbolic space of dimensions three and greater and algebraic integers is investigated. In particular, a certain geometric convergence of fundamental domains for cocompact hyperbolic Coxeter groups with finite-volume limiting polyhedron provides a relation between Salem numbers and Pisot numbers. Several examp...

Let G be a complete Kac–Moody group of rank n ≥ 2 such that the Weyl group of G is a free product of cyclic groups of order 2. We construct new families of examples of cocompact lattices in G, many of which act transitively on the chambers of the building for G.