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

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 $Sp(2g,\mathbb{Z})$-module.

13 pages, 2 figures; minor corrections; to appear in Math. Ann