The Mod two cohomology of the moduli space of rank two stable bundles on a surface and skew Schur polynomials

Christopher W. Scaduto, Matthew Stoffregen

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)683-715
Number of pages33
JournalCanadian Journal of Mathematics
Volume71
Issue number3
DOIs
StatePublished - 2019
Externally publishedYes

Keywords

  • Mod two cohomology
  • Skew schur polynomial
  • Stable bundles

ASJC Scopus subject areas

  • Mathematics(all)

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