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The Mod Two Cohomology of the Moduli Space of Rank Two Stable Bundles on a Surface and Skew Schur Polynomials

Part of: Families, fibrations Differential topology

Published online by Cambridge University Press:  07 January 2019

Christopher W. Scaduto  and
Matthew Stoffregen
Christopher W. Scaduto
Affiliation:
Simons Center for Geometry and Physics, SUNY, Stony Brook, NY 11794-3636, USA Email: cscaduto@scgp.stonybrook.edu
Matthew Stoffregen
Affiliation:
Department of Mathematics, UCLA, Los Angeles, CA 90095, USA Email: mstoff@mit.edu
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Abstract

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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.

Keywords

stable bundlesmod two cohomologyskew schur polynomial

MSC classification

Primary: 14D20: Algebraic moduli problems, moduli of vector bundles
Secondary: 57R58: Floer homology
Type
Article
Information
Canadian Journal of Mathematics , Volume 71 , Issue 3 , June 2019 , pp. 683 - 715
Copyright
© Canadian Mathematical Society 2018 

Footnotes

Author C. S. was supported by NSF grant DMS-1503100.

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