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

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

2008-06-11

arxiv.org/abs/0806.1975v4

The Quarterly Journal of Mathematics 2009

Mathematics

Symplectic Geometry

23 pages - some reviewer recommended edits, a "proof" is upgraded to a proof

Scientific paper

10.1093/qmath/han040

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(\pi_1(X),SU(2)) modulo conjugation by SU(2). In particular, we compute the (rational) equivariant cohomology ring of Hom(\pi_1(X),SU(2)) and use this to compute the ordinary cohomology groups of the quotient Hom(\pi_1(X),SU(2))/SU(2). A key property is that the conjugation action is equivariantly formal.

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