2002/07/31 by Martin Olbrich, Olbrich, Martin
Mathematics · #22E40 #57R19 #58J #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Representation Theory (math.RT) #math.DG #math.RT #msc:22E40 #msc:57R19 #msc:58J
paper · pdf · doi:10.48550/arxiv.math/0207301
121 pages
arxiv created 2002/07/31 · openalex publication_date 2002/07/31 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 L2-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.