The second rational homology of the Torelli group is finitely generated

Abstract

We prove that second rational homology of the Torelli group of an orientable closed surface of genus g is finite dimensional for g at least 51. This rules out the simplest obstruction to the Torelli group being finitely presented and provides a partial answer to a question of Bestvina.

This work has been subsumed and significantly improved upon by work of the author and Putman. This work is a permanent preprint