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Cohomology of convex cocompact groups and invariant distributions on limit sets

Martin Olbrich
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Abstract

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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Martin Olbrich. 2002-07-31. Cohomology of convex cocompact groups and invariant distributions on limit sets. https://arxiv.org/abs/math/0207301

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