Title

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

Document Type

Article

Publication Date

2017

Keywords

automorphism group of free group, Torelli group

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.

Comments

Principal Investigator: Matthew Day

Acknowledgements: Day was supported in part by NSF grant DMS-1206981 and Putman was supported in part by NSF grant DMS-1255350 and the Alfred P Sloan Foundation.

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