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$2n\geqslant 6$. 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.