Donaldson, S. K. Self-dual connections and the topology of smooth 4-manifolds. (English) Zbl 0519.57012 Bull. Am. Math. Soc., New Ser. 8, 81-83 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 3 ReviewsCited in 17 Documents 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 Keywords:oriented cobordism; gauge theory; moduli space; singularities; intersection form of a smooth, compact, simply connected oriented four- dimensional manifold; Kummer surface; failure of smooth surgery in four dimensions; exotic differentiable structures on 4-space; Yang-Mills theory; gauge equivalence classes of smooth connections; self-dual connections; first Stiefel-Whitney class for the analytic index of family of elliptic differential operators Citations:Zbl 0507.57010; Zbl 0046.407; Zbl 0496.57007; Zbl 0484.53026; Zbl 0491.58032; Zbl 0389.53011 × Cite Format Result Cite Review PDF Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.