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Path-connected Yang-Mills moduli spaces. (English) Zbl 0551.53040
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

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
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