Abelian covers of surfaces and the homology of the Torelli group
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908292533452800 |
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| author | Minahan, Daniel Putman, Andrew |
| author_facet | Minahan, Daniel Putman, Andrew |
| contents | We study the first homology group of the mapping class group and Torelli group with coefficients in the first rational homology group of the universal abelian cover of the surface. We prove two contrasting results: for surfaces with one boundary component these twisted homology groups are finite-dimensional, but for surfaces with one puncture they are infinite-dimensional. These results play an important role in a recent paper of the authors calculating the second rational homology group of the Torelli group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00215 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Abelian covers of surfaces and the homology of the Torelli group Minahan, Daniel Putman, Andrew Geometric Topology Algebraic Topology We study the first homology group of the mapping class group and Torelli group with coefficients in the first rational homology group of the universal abelian cover of the surface. We prove two contrasting results: for surfaces with one boundary component these twisted homology groups are finite-dimensional, but for surfaces with one puncture they are infinite-dimensional. These results play an important role in a recent paper of the authors calculating the second rational homology group of the Torelli group. |
| title | Abelian covers of surfaces and the homology of the Torelli group |
| topic | Geometric Topology Algebraic Topology |
| url | https://arxiv.org/abs/2504.00215 |