Equivariant group presentations and the second homology group of the Torelli group

preprint2019arXivOpen access

Abstract

We develop a theory of equivariant group presentations and relate them to the second homology group of a group. Our main application says that the second homology group of the Torelli subgroup of the mapping class group is finitely generated as an Sp(2g,Z)Sp(2g,\mathbb{Z})-module.

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