Orientability in Yang-Mills Theory over Nonorientable Surfaces
Abstract
In arXiv:math/0605587, the first two authors have constructed a gauge-equivariant Morse stratification on the space of connections on a principal U(n)-bundle over a connected, closed, nonorientable surface. This space can be identified with the real locus of the space of connections on the pullback of this bundle over the orientable double cover of this nonorientable surface. In this context, the normal bundles to the Morse strata are real vector bundles. We show that these bundles, and their associated homotopy orbit bundles, are orientable for any n when the nonorientable surface is not homeomorphic to the Klein bottle, and for n<4 when the nonorientable surface is the Klein bottle. We also derive similar orientability results when the structure group is SU(n).
Keywords
Cite
@article{arxiv.0810.4882,
title = {Orientability in Yang-Mills Theory over Nonorientable Surfaces},
author = {Nan-Kuo Ho and Chiu-Chu Melissa Liu and Daniel A. Ramras},
journal= {arXiv preprint arXiv:0810.4882},
year = {2010}
}
Comments
49 pages, 3 figures