|
| Homology stability for outer automorphism groups of free groups |
| Allen Hatcher and Karen Vogtmann |
| Algebr. Geom. Topol. 4 (2004), 1253-1272.
|
| |
| We prove that the quotient map from the automorphism group to the outer automorphism group of the free group of rank n is an isomorphism on homology in dimension i for n at least 2i+4. This corrects an earlier proof by the first author and improves the stability range. In the course of the proof, we also prove homology stability for a sequence of groups which are natural analogs of mapping class groups of surfaces with boundary. In particular, this leads to a slight improvement on the known stability range for Aut(F_n), showing that its ith homology is independent of n for n at least 2i+2. |
|