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The Wild World Of 4-manifolds - 9780821837498

Un libro in lingua di Alexandru Scorpan edito da Amer Mathematical Society, 2005

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Billing his work as a pleasant-to-read global picture of the differential topology of dimension 4, the author is primarily concerned with smooth simply-connected, closed oriented 4-manifolds. After presenting the main technique used for dealing with higher-dimensional manifolds, the h -cobordism theorem, he covers aspects of the main invariant of the main invariant of a 4-manifold, its intersection form, including discussion of the K3 complex surface, the relationship of intersection forms with the topology of the 4- manifolds, and Freedman's classification of topological 4-manifolds. Next, the geometry of complex surfaces is reviewed as a preliminary to discussion of results from the application of gauge theory to 4-manifolds, which includes examinations of Seiberg-Witten theory, Taubes' interpretation on symplectic manifolds, the problem of determining the minimum genus needed to represent a fixed homology class by embedded surfaces in a 4-manifold, and a construction that yields infinite families of homeomorphic but non-diffeomorphic 4-manifolds. Annotation ©2005 Book News, Inc., Portland, OR (booknews.com)

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