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arXiv · 0806.1975

The moduli space of flat SU(2)-bundles over a nonorientable surface

Thomas Baird
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Abstract

We study the topology of the moduli space of flat SU(2)-bundles over a nonorientable surface X. This moduli space may be identified with the space of homomorphisms Hom(π_1(X),SU(2)) modulo conjugation by SU(2). In particular, we compute the (rational) equivariant cohomology ring of Hom(π_1(X),SU(2)) and use this to compute the ordinary cohomology groups of the quotient Hom(π_1(X),SU(2))/SU(2). A key property is that the conjugation action is equivariantly formal.

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Thomas Baird. 2008-12-31. The moduli space of flat SU(2)-bundles over a nonorientable surface. https://doi.org/10.1093/qmath/han040

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