Calculating the second rational cohomology group of the Torelli group
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866914511261270016 |
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| author | Putman, Andrew |
| author_facet | Putman, Andrew |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24733 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Calculating the second rational cohomology group of the Torelli group Putman, Andrew Geometric Topology Algebraic Topology 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. |
| title | Calculating the second rational cohomology group of the Torelli group |
| topic | Geometric Topology Algebraic Topology |
| url | https://arxiv.org/abs/2604.24733 |