Finiteness of classifying spaces of relative diffeomorphism groups of 3manifolds
Abstract
The main theorem shows that if M is an irreducible compact connected orientable 3manifold with nonempty boundary, then the classifying space BDiff(M rel dM) of the space of diffeomorphisms of M which restrict to the identity map on boundary(M) has the homotopy type of a finite aspherical CWcomplex. This answers, for this class of manifolds, a question posed by M Kontsevich. The main theorem follows from a more precise result, which asserts that for these manifolds the mapping class group H(M rel dM) is built up as a sequence of extensions of free abelian groups and subgroups of finite index in relative mapping class groups of compact connected surfaces.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 December 1997
 DOI:
 10.48550/arXiv.math/9712260
 arXiv:
 arXiv:math/9712260
 Bibcode:
 1997math.....12260H
 Keywords:

 Mathematics  Geometric Topology;
 57M99;
 55R35;
 58D99
 EPrint:
 19 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol1/paper7.abs.html