The Mod Two Cohomology of the Moduli Space of Rank Two Stable Bundles on a Surface and Skew Schur Polynomials
| Autor: | Matthew Stoffregen, Christopher Scaduto |
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| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Rank (linear algebra) General Mathematics Riemann surface 010102 general mathematics 01 natural sciences Cohomology Schur's theorem Cohomology ring Schur polynomial Moduli space Algebra symbols.namesake 0103 physical sciences symbols Equivariant cohomology 010307 mathematical physics 0101 mathematics Mathematics |
| Zdroj: | Canadian Journal of Mathematics. 71:683-715 |
| ISSN: | 1496-4279 0008-414X |
| DOI: | 10.4153/cjm-2017-050-7 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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