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The moduli space of stable vector bundles over a real algebraic curve

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Abstract

We study the spaces of stable real and quaternionic vector bundles on a real algebraic curve. The basic relationship is established with unitary representations of an extension of \({\mathbb{Z}/2}\) by the fundamental group. By comparison with the space of real or quaternionic connections, some of the basic topological invariants of these spaces are calculated.

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Authors and Affiliations

  1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Rd, Mumbai, 400005, India

    Indranil Biswas

  2. Département de Mathématiques, Laboratoire CNRS UMR 6205, Université de Bretagne Occidentale, 6 avenue Victor Le Gorgeu, CS 93837, 29238, Brest cedex 3, France

    Johannes Huisman

  3. Department of Mathematics, McGill University, Burnside Hall, 805 Sherbrooke Street West, Montreal, QC, H3A 2K6, Canada

    Jacques Hurtubise

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  1. Indranil Biswas
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  2. Johannes Huisman
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  3. Jacques Hurtubise
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Correspondence to Jacques Hurtubise.

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Biswas, I., Huisman, J. & Hurtubise, J. The moduli space of stable vector bundles over a real algebraic curve. Math. Ann. 347, 201–233 (2010). https://doi.org/10.1007/s00208-009-0442-5

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  • DOI: https://doi.org/10.1007/s00208-009-0442-5

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