Path-connected Yang-Mills moduli spaces (Q801310)

In this paper it is proved that the moduli spaces of self-dual connections on SU(2) or SU(3) bundles over \(S^ 4\) are path-connected. The proof uses the mini-max technique of the calculus of variations, but since the Yang-Mills functional does not satisfy the Palais-Smale condition C, the author has to make a careful analysis in order to apply Ljusternik-Schnirelman type arguments. But for the situation at hand, which is a threshold case were the standard Morse-theory just fails, the author could still get some results for fields of low energy. Combining these with some estimates for the index and a grafting procedure he arrives at the result.