On the cohomology of Torelli groups. II

TL;DR

This paper investigates the algebraic structure of the rational cohomology of Torelli groups associated with certain high-dimensional manifolds, providing new insights into their ring structure in a stable range.

Contribution

It describes the ring structure of the rational cohomology of Torelli groups for manifolds of the form ^g S^n imes S^n in a stable range, extending previous results to include the case 2n=2.

Findings

Ring structure of the rational cohomology described in a stable range

Results applicable to manifolds with 2n  6, including 2n=2

Connections to unpublished results of Kawazumi and Morita

Abstract

We describe the ring structure of the rational cohomology of the Torelli groups of the manifolds $\#^g S^n \times S^n$ in a stable range, for $2n \geq 6$. Some of our results are also valid for $2n=2$, where they are closely related to unpublished results of Kawazumi and Morita.