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arXiv · 1704.04449

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

Jeremy Miller·Peter Patzt·Jennifer C. H. Wilson
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Abstract

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.

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BibTeXRIS

Jeremy Miller, Peter Patzt, Jennifer C. H. Wilson. 2017-04-14. Central stability for the homology of congruence subgroups and the second homology of Torelli groups. https://doi.org/10.1016/j.aim.2019.106740

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