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# Moduli Spaces of Vector Bundles over a Real Curve: $\mathbb Z/2$-Betti Numbers

Published:2014-04-21
Printed: Oct 2014
• Thomas Baird,
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL, A1C 5S7
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## Abstract

Moduli spaces of real bundles over a real curve arise naturally as Lagrangian submanifolds of the moduli space of semi-stable bundles over a complex curve. In this paper, we adapt the methods of Atiyah-Bott's Yang-Mills over a Riemann Surface'' to compute $\mathbb Z/2$-Betti numbers of these spaces.
 Keywords: cohomology of moduli spaces, holomorphic vector bundles
 MSC Classifications: 32L05 - Holomorphic bundles and generalizations 14P25 - Topology of real algebraic varieties