Virtually geometrically finite mapping class groups of 3-manifolds

Abstract

If M is a compact orientable irreducible sufficiently large 3-manifold, then the mapping class group ℋ(M) contains a subgroup of finite index which is the fundamental group of a finite aspherical CW-complex. If in addition the boundary of M is incompressible, then ℋ(M) contains a subgroup of finite index which is a duality group. For many cases, the virtual cohomological dimension of ℋ(M) is calculated. © 1991, International Press of Boston, Inc. All Rights Reserved.