# On the cohomology of Torelli groups

## TL;DR

This paper provides a complete description of the algebraic rational cohomology of Torelli groups for certain high-dimensional manifolds within a stable range, extending to low dimensions under finiteness assumptions.

## Contribution

It offers the first full algebraic rational cohomology calculation for Torelli groups of connected sums of spheres, in a stable range, for dimensions greater than or equal to 6.

## Key findings

- Explicit algebraic description of the cohomology groups
- Validity of results for low dimensions under finiteness assumptions
- Extension of known results to a broader class of manifolds

## Abstract

We completely describe the algebraic part of the rational cohomology of the Torelli groups of the manifolds $\#^g S^n \times S^n$ relative to a disc in a stable range, for $2n \geq 6$. Our calculation is also valid for $2n=2$ assuming that the rational cohomology groups of these Torelli groups are finite dimensional in a stable range.