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arXiv:1408.6242 [math.GT]AbstractReferencesReviewsResources

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

Matthew B. Day, Andrew Putman

Published 2014-08-26Version 1

Let IA_n be the Torelli subgroup of Aut(F_n). We give an explicit finite set of generators for H_2(IA_n) as a GL_n(Z)-module. Corollaries include a version of surjective representation stability for H_2(IA_n), the vanishing of the GL_n(Z)-coinvariants of H_2(IA_n), and the vanishing of the second rational homology group of the level l congruence subgroup of Aut(F_n). Our generating set is derived from a new group presentation for IA_n which is infinite but which has a simple recursive form.

Comments: 39 pages
Categories: math.GT, math.AT, math.GR
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