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Compactness of the moduli space of Yang-Mills connections in higher dimensions. (English) Zbl 0647.53030
In this paper the author generalizes K. K. Uhlenbeck’s [Commun. Math. Phys. 83, 31-42 (1982; Zbl 0499.58019)] compactness theorem for the moduli space of Yang-Mills connections to higher dimensions. Namely, let \(\{A_ i\}\) be a sequence of Yang-Mills connections with uniform \(L^ 2\)-bounds on curvatures on a bundle P over a compact Riemannian manifold M of dimension n. Then there exists a subsequence of \(\{A_ i\}\) which converges after gauge transformations outside a compact set S with finite (n-4)-dimensional Hausdorff measure.
Reviewer: H.Nakajima

MSC:
53C20 Global Riemannian geometry, including pinching
53C05 Connections (general theory)
58D17 Manifolds of metrics (especially Riemannian)
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