2007/11/30 by Igor Belegradek, Belegradek, Igor · 2 citations
Mathematics · #20F65 #22E40 #57R19 #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Group Theory (math.GR) #math.AT #math.DG #math.GR #msc:20F65 #msc:22E40 #msc:57R19
paper · pdf · doi:10.48550/arxiv.0711.5001
37 pages, to appear in Math. Annalen
openalex publication_date 2007/11/30 · arxiv created 2010/08/28 · arxiv updated 2010/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study spaces obtained from a complete finite volume complex hyperbolic n-manifold M by removing a compact totally geodesic complex (n-1)-submanifold. The main result is that the fundamental group of M-S is relatively hyperbolic, relative to fundamental groups of the ends of M-S, and M-S admits a complete finite volume A-regular Riemannian metric of negative sectional curvature. It follows that for n>1 the fundamental group of M-S satisfies Mostow-type Rigidity, has finite asymptotic dimension and rapid decay property, satisfies Borel and Baum-Connes conjectures, is co-Hopf and residually hyperbolic, has no nontrivial subgroups with property (T), and has finite outer automorphism group. Furthermore, if M is compact, then the fundamental group of M-S is biautomatic and satisfies Strong Tits Alternative.