Cohomology of convex cocompact groups and invariant distributions on limit sets

Details Cohomology of convex cocompact groups and invariant distributions on limit sets Cohomology of convex cocompact groups and invariant distributions on limit sets

2002-07-31

arxiv.org/abs/math/0207301v1

Mathematics

Differential Geometry

121 pages

Scientific paper

This paper contains a thorough investigation of invariant distributions supported on limit sets of discrete groups acting convex cocompactly on symmetric spaces of negative curvature. It can be considered as a continuation of math.DG/9810146. Based on this investigation we provide proofs of the Hodge theoretic results for the cohomology of real hyperbolic manifolds announced in math.DG/0009038, improve the bounds for the critical exponents obtained by Corlette for the quaternionic and the Cayley case, compute the L^2-cohomology for the corresponding locally symmetric spaces, prove a version of the Harder-Borel conjecture for real hyperbolic manifolds, and compute higher cohomology groups with coefficients in hyperfunctions supported on the limit set.

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