A spectral sequence determining the homology of $\mathrm{Out}(F_n)$ in terms of its mapping class subgroups

Matthew Horak

Vol. 227 (2006), No. 1, 65–93

DOI: 10.2140/pjm.2006.227.65

Abstract

We construct a covering of the spine of the Culler–Vogtmann outer space Out($F_n$) by complexes of ribbon graphs. By considering the equivariant homology for the action of Out($F_n$) on this covering, we construct a spectral sequence converging to the homology of Out($F_n$) that has its $E^1$ terms given by the homology of mapping class groups and their subgroups. This spectral sequence can be seen as encoding all of the information of how the homology of Out($F_n$) is related to the homology of mapping class groups and their subgroups

Keywords

free group automorphisms, mapping class groups, ribbon graphs

Mathematical Subject Classification 2000

Primary: 20F65

Secondary: 57M07

Milestones

Received: 2 July 2004

Accepted: 31 January 2006

Published: 1 September 2006