Rigidity and relative hyperbolicity of real hyperbolic hyperplane complements

Details Rigidity and relative hyperbolicity of real hyperbolic hyperplane complements Rigidity and relative hyperbolicity of real hyperbolic hyperplane complements

2007-11-15

arxiv.org/abs/0711.2324v4

Mathematics

Group Theory

to appear in Pure and Applied Mathematics Quarterly in the special issue in honor of Farrell and Jones

Scientific paper

For n>3 we study spaces obtained from finite volume complete real hyperbolic n-manifolds by removing a compact totally geodesic submanifold of codimension two. We prove that their fundamental groups are relative hyperbolic, co-Hopf, biautomatic, residually hyperbolic, not K\"ahler, not isomorphic to lattices in virtually connected real Lie groups, have no nontrivial subgroups with property (T), have finite outer automorphism groups, satisfy Mostow-type Rigidity, have finite asymptotic dimension and rapid decay property, and satisfy Baum-Connes conjecture. We also characterize those lattices in real Lie groups that are isomorphic to relatively hyperbolic groups.

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