Resumen de A spectral sequence determining the homology of Out(Fn) in terms of its mapping class subgroups

Matthew Horak

• We construct a covering of the spine of the Culler¿Vogtmann outer space Out(Fn) by complexes of ribbon graphs. By considering the equivariant homology for the action of Out(Fn) on this covering, we construct a spectral sequence converging to the homology of Out(Fn) that has its E1 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(Fn) is related to the homology of mapping class groups and their subgroups