Calculating the second rational cohomology group of the Torelli group
Geometric Topology
2026-04-28 v1 Algebraic Topology
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.
Cite
@article{arxiv.2604.24733,
title = {Calculating the second rational cohomology group of the Torelli group},
author = {Andrew Putman},
journal= {arXiv preprint arXiv:2604.24733},
year = {2026}
}
Comments
58 pages, 30 figures