Countable groups are mapping class groups of hyperbolic 3-manifolds

2005/09/14 by Roberto Frigerio, Bruno Martelli, Frigerio, Roberto +1
Mathematics · #20F29 #30F40 (secondary) #57M50 (primary) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT #msc:20F29 #msc:30F40 #msc:57M50

paper · pdf · doi:10.48550/arxiv.math/0509311

15 pages, 6 figures

arxiv created 2005/09/14 · arxiv updated 2009/12/01

Abstract

We prove that for every countable group G there exists a hyperbolic 3-manifold M such that the isometry group of M, the mapping class group of M, and the outer automorphism group of the fundamental group of M are isomorphic to G.

Related

• Hyperbolic 2-dimensional manifolds with 3-dimensional automorphism groups
• Finite-volume hyperbolic 3-manifolds are almost determined by their finite quotient groups
• Finite groups and complex projective surfaces
• Determining hyperbolic 3-manifolds by their surfaces
• The congruence subgroup property for mapping class groups and the residual finiteness of hyperbolic groups