Homological stability for automorphism groups

Nathalie Wahl

Published 2014-09-11Version 1

We prove a general homological stability theorem for families of automorphism groups in certain categories. We show that this theorem can be applied to all the classical examples of stable families of groups, such as the symmetric groups, general linear groups and mapping class groups, and obtain new stability theorems with twisted coefficients for the braid groups, automorphisms of free groups, mapping class groups of non-orientable surfaces and mapping class groups of 3-manifolds.