English

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.

Keywords

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

R2 v1 2026-06-21T10:49:47.325Z