Mon, 12 Nov 2007
13:15
13:15
L3
Forthcoming events in this series
Abstract:
(joint work with Allen Hatcher) Let M be a compact, connected 3-manifold with a
fixed boundary component d_0M. For each prime manifold P, we consider the
mapping class group of the manifold M_n^P obtained from M by taking a connected
sum with n copies of P. We prove that the ith homology of this mapping class
group is independent of n in the range n>2i+1. Our theorem moreover applies to
certain subgroups of the mapping class group and include, as special cases,
homological stability for the automorphism groups of free groups and of other
free products, for the symmetric groups and for wreath products with symmetric
groups.