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arXiv:1704.04449 [math.AT]AbstractReferencesReviewsResources

Central stability for the homology of congruence subgroups and the second homology of Torelli groups

Jeremy Miller, Peter Patzt, Jennifer C. H. Wilson

Published 2017-04-14Version 1

We prove a representation stability result for the second homology groups of Torelli subgroups of mapping class groups and automorphism groups of free groups. This strengthens the results of Boldsen-Hauge Dollerup and Day-Putman. We also prove a new representation stability result for the homology of certain congruence subgroups, partially improving upon the work of Putman-Sam. These results follow from a general theorem on syzygies of certain modules with finite polynomial degree.

Comments: 34 pages, 3 figures. Comments welcome
Categories: math.AT, math.GR, math.GT, math.RT
Subjects: 20J06, 11F75, 18A25, 55U10
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