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The Quarterly Journal of Mathematics Advance Access published online on January 21, 2009
The Quarterly Journal of Mathematics, doi:10.1093/qmath/han040
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© 2009. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

MODULI SPACES OF FLAT SU(2)-BUNDLES OVER NON-ORIENTABLE SURFACES

Thomas John Baird{dagger}

Department of Mathematics, University of Toronto, Toronto, Ont., Canada M5S 2E4

{dagger} Presently at Mathematical Institute, University of Oxford, 24–29 St. Giles, Oxford OX1 3LB, UK. E-mail: baird{at}maths.ox.ac.uk

Received 1 December 2008;
  Abstract

We study the topology of the moduli space of flat SU (2)-bundles over a non-orientable surface {Sigma}. This moduli space may be identified with the space of homomorphisms Hom ({pi}1({Sigma}), SU (2)) modulo conjugation by SU (2). In particular, we compute the (rational) equivariant cohomology ring of Hom ({pi}1({Sigma}), SU (2)) and use this to compute the ordinary cohomology groups of the quotient Hom ({pi}1({Sigma}), SU (2))/SU (2). A key property is that the conjugation action is equivariantly formal.


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