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Self-dual connections and the topology of smooth 4-manifolds. (English) Zbl 0519.57012


MSC:

57N13 Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010)
58J20 Index theory and related fixed-point theorems on manifolds
53C05 Connections (general theory)
57R55 Differentiable structures in differential topology
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
57R19 Algebraic topology on manifolds and differential topology
57R20 Characteristic classes and numbers in differential topology
53C80 Applications of global differential geometry to the sciences
81T08 Constructive quantum field theory
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References:

[1] M. F. Atiyah, N. J. Hitchin, and I. M. Singer, Self-duality in four-dimensional Riemannian geometry, Proc. Roy. Soc. London Ser. A 362 (1978), no. 1711, 425 – 461. · Zbl 0389.53011 · doi:10.1098/rspa.1978.0143
[2] M. Kuranishi, New proof for the existence of locally complete families of complex structures, Proc. Conf. Complex Analysis (Minneapolis, 1964) Springer, Berlin, 1965, pp. 142 – 154.
[3] John Milnor, On simply connected 4-manifolds, Symposium internacional de topología algebraica International symposi um on algebraic topology, Universidad Nacional Autónoma de México and UNESCO, Mexico City, 1958, pp. 122 – 128. · Zbl 0105.17204
[4] J.-P. Serre, A course in arithmetic, Springer-Verlag, New York-Heidelberg, 1973. Translated from the French; Graduate Texts in Mathematics, No. 7. · Zbl 0256.12001
[5] S. Smale, An infinite dimensional version of Sard’s theorem, Amer. J. Math. 87 (1965), 861 – 866. · Zbl 0143.35301 · doi:10.2307/2373250
[6] C. H. Taubes, The existence of self-dual connections on non self-dual 4-manifolds, J. Differential Geom. (to appear). · Zbl 0484.53026
[7] K. K. Uhlenbeck, Connections vnth L, Comm. Math. Phys. 3 (1981).
[8] Karen K. Uhlenbeck, Removable singularities in Yang-Mills fields, Comm. Math. Phys. 83 (1982), no. 1, 11 – 29. · Zbl 0491.58032
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