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

  • Christopher W. Scaduto,
    Simons Center for Geometry and Physics, State University of New York, Stony Brook, NY 11794-3636, USA
  • Matthew Stoffregen,
    Department of Mathematics, University of California, Los Angeles, Los Angeles, CA 90095, USA
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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.
Keywords: stable bundle, mod two cohomology, skew schur polynomial stable bundle, mod two cohomology, skew schur polynomial
MSC Classifications: 14D20, 57R58 show english descriptions Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}
Floer homology
14D20 - Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}
57R58 - Floer homology
 

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