Mapping class subgroups of Out(F_n)

Details Mapping class subgroups of Out(F_n) Mapping class subgroups of Out(F_n)

2003-10-21

arxiv.org/abs/math/0310328v2

Pacific Journal of Mathematics, 227 (2007), No. 1, 65-94

Mathematics

Geometric Topology

Improved historical background, figure added to Section 3, proofs in Section 5 clarified

Scientific paper

We construct a covering of Culler-Vogtmann Outer space by the Teichmuller spaces of punctured surfaces. 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 E^1 terms given by the homology of mapping class groups and groups that are, up to finite index, subgroups of mapping class groups. 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.

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