The Yang-Mills stratification for surfaces revisited

Details The Yang-Mills stratification for surfaces revisited The Yang-Mills stratification for surfaces revisited

2008-05-16

arxiv.org/abs/0805.2587v4

Mathematics

Differential Geometry

18 pages. A shorter version will appear in Proc. AMS. V. 4: minor changes due to referee's comments; Section 3, on tubular nei

Scientific paper

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.

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