The Yang-Mills stratification for surfaces revisited
Abstract
We revisit Atiyah and Bott's study of Morse theory for the Yang-Mills functional over a Riemann surface, and establish new formulas for the minimum codimension of a (non-semi-stable) stratum. These results yield the exact connectivity of the natural map (C_{min} E)//G(E) --> Map^E (M, BU(n)) from the homotopy orbits of the space of central Yang-Mills connections to the classifying space of the gauge group G(E). All of these results carry over to non-orientable surfaces via Ho and Liu's non-orientable Yang-Mills theory. A somewhat less detailed version of this paper (titled "On the Yang-Mills stratification for surfaces") will appear in the Proceedings of the AMS.
Cite
@article{arxiv.0805.2587,
title = {The Yang-Mills stratification for surfaces revisited},
author = {Daniel A. Ramras},
journal= {arXiv preprint arXiv:0805.2587},
year = {2018}
}
Comments
18 pages. A shorter version has appeared in Proc. AMS. V. 4: minor changes due to referee's comments; Section 3, on tubular neighborhoods, has been moved arXiv:1006.0063, which fills a gap regarding local triviality of normal bundles. V. 3: changed formatting, small correction to Theorem 4.11. V.2: changed formatting; revised the introduction; minor simplifications to the proof of Proposition 4.1