The cohomology of rank two stable bundle moduli: mod two nilpotency & skew Schur polynomials
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2017
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| _version_ | 1866913492405059584 |
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| author | Scaduto, Christopher Stoffregen, Matthew |
| author_facet | Scaduto, Christopher Stoffregen, Matthew |
| contents | We compute cup product pairings in the integral cohomology ring of the moduli space of rank two stable bundles with odd determinant over a Riemann surface using methods of Zagier. The resulting formula is related to a generating function for certain skew Schur polynomials. As an application, we compute the nilpotency degree of a distinguished degree two generator in the mod two cohomology ring. We then give descriptions of the mod two cohomology rings in low genus, and describe the subrings invariant under the mapping class group action. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1707_06207 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | The cohomology of rank two stable bundle moduli: mod two nilpotency & skew Schur polynomials Scaduto, Christopher Stoffregen, Matthew Geometric Topology 14D20, 57R58 We compute cup product pairings in the integral cohomology ring of the moduli space of rank two stable bundles with odd determinant over a Riemann surface using methods of Zagier. The resulting formula is related to a generating function for certain skew Schur polynomials. As an application, we compute the nilpotency degree of a distinguished degree two generator in the mod two cohomology ring. We then give descriptions of the mod two cohomology rings in low genus, and describe the subrings invariant under the mapping class group action. |
| title | The cohomology of rank two stable bundle moduli: mod two nilpotency & skew Schur polynomials |
| topic | Geometric Topology 14D20, 57R58 |
| url | https://arxiv.org/abs/1707.06207 |