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.

arXiv comment57 pages; v2 improved exposition and minor mathematical corrections; v3; v4 final version, to appear in Forum of Mathematics, Pi

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Cited by in corpus (8)

• Central stability for the homology of congruence subgroups and the second homology of Torelli groups
• The cohomology of Torelli groups is algebraic
• Borel's stable range for the cohomology of arithmetic groups
• On spectral sequence for the action of genus 3 Torelli group on the complex of cycles
• Abelian Cycles in the Homology of the Torelli group
• A note on rational homological stability for automorphisms of manifolds
• Some rational homology computations for diffeomorphisms of odd-dimensional manifolds
• Stable twisted cohomology of the mapping class groups in the unit tangent bundle homology