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Introduction to the geometry and topology of Yang-Mills fields. (Introduzione alla geometria e alla topologia dei campi di Yang-Mills). (Italian. English summary) Zbl 0598.57001

This is an expository paper on the physical origins of the Yang-Mills theory and on its recent spectacular applications to 4-dimensional topology, discovered by S. Donaldson. A lengthy appendix shows how the basic results of A. Casson, M. Freedman and S. Donaldson imply the existence of exotic \({\mathbb{R}}^ 4s\). No specialized background is required from the reader of this paper.

MSC:

57-02 Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes
53C80 Applications of global differential geometry to the sciences
57N13 Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010)