2007/11/14 by Igor Belegradek, Belegradek, Igor
Mathematics · #20F65 (Primary) #22E40 (Secondary) #57R19 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Group Theory (math.GR) #Mathematical Dynamics and Fractals #math.DG #math.GR #msc:20F65 #msc:22E40 #msc:57R19
paper · pdf · doi:10.48550/arxiv.0711.2324
to appear in Pure and Applied Mathematics Quarterly in the special issue in honor of Farrell and Jones
openalex publication_date 2007/11/14 · arxiv created 2010/08/28 · arxiv updated 2010/08/31 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
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 Kähler, 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.