On the second homology group of the Torelli subgroup of Aut(Fn)
automorphism group of free group, Torelli group
Let IAn be the Torelli subgroup of Aut(Fn). We give an explicit finite set of generators for H2(IAn) as a GLn(Z)–module. Corollaries include a version of surjective representation stability for H2(IAn), the vanishing of the GLn(Z)–coinvariants of H2(IAn), and the vanishing of the second rational homology group of the level ℓ congruence subgroup of Aut(Fn). Our generating set is derived from a new group presentation for IAn which is infinite but which has a simple recursive form.
Day, Matthew B. and Putman, Andrew, "On the second homology group of the Torelli subgroup of Aut(Fn)" (2017). Mathematical Sciences Faculty Publications and Presentations. 1.