The moduli space of flat SU(2)-bundles over a nonorientable surface
Symplectic Geometry
2009-02-06 v4 Algebraic Topology
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(\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.
Cite
@article{arxiv.0806.1975,
title = {The moduli space of flat SU(2)-bundles over a nonorientable surface},
author = {Thomas Baird},
journal= {arXiv preprint arXiv:0806.1975},
year = {2009}
}
Comments
23 pages - some reviewer recommended edits, a "proof" is upgraded to a proof