On the second homology group of the Torelli subgroup of Aut(Fn)
Abstract
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.
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