Taubes, Clifford Henry Path-connected Yang-Mills moduli spaces. (English) Zbl 0551.53040 J. Differ. Geom. 19, 337-392 (1984). 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. Reviewer: M.Min-Oo Cited in 2 ReviewsCited in 37 Documents MSC: 53C80 Applications of global differential geometry to the sciences 58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces 81T08 Constructive quantum field theory 53C05 Connections (general theory) Keywords:Ljusternik-Schnirelman theory; moduli spaces; self-dual connections; Yang-Mills functional PDFBibTeX XMLCite \textit{C. H. Taubes}, J. Differ. Geom. 19, 337--392 (1984; Zbl 0551.53040) Full Text: DOI