The Mod Two Cohomology of the Moduli Space of Rank Two Stable Bundles on a Surface and Skew Schur Polynomials. (7th January 2019)

• Record Type: Journal Article
• Authors: Scaduto, Christopher W.; Stoffregen, Matthew
• Is Part Of: Canadian journal of mathematics. Volume 71:Number 3(2019)
• Page Start: 683
• Page End: 715
• Publication Date: 2019-01-07
• Subjects: 14D20, -- 57R58; stable bundles, -- mod two cohomology, -- skew schur polynomial; Mathematics -- Periodicals; Mathematics; Electronic journals; Periodicals; 510
• DOI: 10.4153/CJM-2017-050-7
• Languages: English
• ISSNs: 0008-414X

Abstract

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.