On the cohomology of Torelli groups

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 $2n\ge 6$. 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.

57 pages; v2 improved exposition and minor mathematical corrections; v3; v4 final version, to appear in Forum of Mathematics, Pi