We prove a vanishing theorem for a convex cocompact hyperbolic manifold, which relates its L cohomology and the Hausdorff dimension of its limit set. The borderline case is shown to characterize the manifold completely.

We prove a vanishing theorem for a convex cocompact hyperbolic manifold which relates its L2-cohomology and the Hausdorff dimension of its limit set. The borderline case is shown to characterize the manifold completely.

Let G be a locally compact group with cocompact connected component. We prove that the assembly map from the topological K-theory of G to the K-theory of the reduced C *-algebra of G is an isomorphism.

In this paper we study geodesic Ptolemy metric spaces X which allow proper and cocompact isometric actions of crystallographic or, more generally, virtual polycyclic groups. We show that X is equivariantly rough isometric to a Euclidean space.

Let S be a compact orientable surface, and Mod(S) its mapping class group. Then there exists a constant M(S), which depends on S, with the following property. Suppose a, b ∈ Mod(S) are independent (i.e., [a, b] 6= 1 for any n,m 6= 0) pseudo-Anosov elements. Then for any n,m ≥ M , the subgroup 〈a, b〉 is free of rank two, and convex-cocompact in the sense of Farb-Mosher. In particular all nontriv...

In the study of Fuchsian groups, it is a nontrivial problem to determine a set of generators. Using a dynamical approach we construct for any cocompact arithmetic Fuchsian group a fundamental region in SL2(R) from which we determine a set of small generators.