On the Torelli Lie algebra

Abstract

We prove two theorems about the Malcev Lie algebra associated to the Torelli group of a surface of genus $g$: stably, it is Koszul and the kernel of the Johnson homomorphism consists only of trivial $S{p}_{2g}(\mathbb{Z})$-representations lying in the centre.

arXiv comment41 pages; v2. 45 pages, accepted version to appear in Forum of Mathematics, Pi