On the Yang–Mills stratification for surfaces
Daniel A. Ramras · Proceedings of the American Mathematical Society · 2010
Atiyah and Bott showed that Morse theory for the Yang–Mills functional can be used to study the space of flat, or more generally central, connections on a bundle over a Riemann surface. These methods have recently been extended to non-orientable surfaces by Ho and Liu. In this article, we use Morse theory to determine the exact connectivity of the natural map from the homotopy orbits of the space of central Yang–Mills connections to the classifying space of the gauge group. The key ingredient in this computation is a combinatorial study of the Morse indices of Yang–Mills critical sets.