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arXiv · 2604.24733

Calculating the second rational cohomology group of the Torelli group

Andrew Putman
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Abstract

Minahan and the author recently proved results that allow the calculation of the second rational cohomology group of the Torelli group. This builds on two key ingredients: Hain's calculation of the image of the cup product pairing on the first cohomology group, and Kupers--Randal-Williams's calculation of the maximal algebraic subrepresentation of the second cohomology group. This paper gives an exposition of both of these results, including prerequisite material about the Johnson homomorphism.

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Andrew Putman. 2026-04-27. Calculating the second rational cohomology group of the Torelli group. https://arxiv.org/abs/2604.24733

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