Mathematical Research Letters

Volume 17 (2010)

Number 5

Moduli of flat SU(3)-bundles over a Klein bottle

Pages: 843 – 849

DOI: https://dx.doi.org/10.4310/MRL.2010.v17.n5.a4

Author

Thomas John Baird (Mathematical Institute, University of Oxford, 24-29 St. Giles' St., Oxford UK, OX1 3LB)

Abstract

In this short note, we compute the Betti numbers of the moduli stack of flat $SU(3)$-bundles over a Klein bottle. We also handle the general compact group case over $\R P^2$. In all cases the cohomology is found to be equivariantly formal, supporting a conjecture from the author’s doctoral thesis. Our results also verify conjectural formulas obtained by Ho-Liu using Yang-Mills Morse theory.

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Published 1 January 2010