04744nam 22007935 450 991014442150332120210913155339.03-540-40952-110.1007/978-3-540-40952-6(CKB)1000000000575758(SSID)ssj0000324391(PQKBManifestationID)12072490(PQKBTitleCode)TC0000324391(PQKBWorkID)10314190(PQKB)10728420(DE-He213)978-3-540-40952-6(MiAaPQ)EBC3087227(PPN)155201840(EXLCZ)99100000000057575820121227d2001 u| 0engurnn#008mamaatxtccrLectures on Seiberg-Witten Invariants /by John D. Moore2nd ed. 2001.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2001.1 online resource (VIII, 121 p.)Lecture Notes in Mathematics,0075-8434 ;1629Bibliographic Level Mode of Issuance: Monograph3-540-41221-2 Includes bibliographical references and index.Riemannian, symplectic and complex geometry are often studied by means ofsolutions to systems ofnonlinear differential equations, such as the equa­ tions of geodesics, minimal surfaces, pseudoholomorphic curves and Yang­ Mills connections. For studying such equations, a new unified technology has been developed, involving analysis on infinite-dimensional manifolds. A striking applications of the new technology is Donaldson's theory of "anti-self-dual" connections on SU(2)-bundles over four-manifolds, which applies the Yang-Mills equations from mathematical physics to shed light on the relationship between the classification of topological and smooth four-manifolds. This reverses the expected direction of application from topology to differential equations to mathematical physics. Even though the Yang-Mills equations are only mildly nonlinear, a prodigious amount of nonlinear analysis is necessary to fully understand the properties of the space of solutions. . At our present state of knowledge, understanding smooth structures on topological four-manifolds seems to require nonlinear as opposed to linear PDE's. It is therefore quite surprising that there is a set of PDE's which are even less nonlinear than the Yang-Mills equation, but can yield many of the most important results from Donaldson's theory. These are the Seiberg-Witte~ equations. These lecture notes stem from a graduate course given at the University of California in Santa Barbara during the spring quarter of 1995. The objective was to make the Seiberg-Witten approach to Donaldson theory accessible to second-year graduate students who had already taken basic courses in differential geometry and algebraic topology.Lecture Notes in Mathematics,0075-8434 ;1629AlgebraAlgebraic topologyCalculus of variationsGlobal analysis (Mathematics)Manifolds (Mathematics)System theoryGeometry, AlgebraicAlgebrahttps://scigraph.springernature.com/ontologies/product-market-codes/M11000Algebraic Topologyhttps://scigraph.springernature.com/ontologies/product-market-codes/M28019Calculus of Variations and Optimal Control; Optimizationhttps://scigraph.springernature.com/ontologies/product-market-codes/M26016Global Analysis and Analysis on Manifoldshttps://scigraph.springernature.com/ontologies/product-market-codes/M12082Systems Theory, Controlhttps://scigraph.springernature.com/ontologies/product-market-codes/M13070Algebraic Geometryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11019Algebra.Algebraic topology.Calculus of variations.Global analysis (Mathematics)Manifolds (Mathematics)System theory.Geometry, Algebraic.Algebra.Algebraic Topology.Calculus of Variations and Optimal Control; Optimization.Global Analysis and Analysis on Manifolds.Systems Theory, Control.Algebraic Geometry.510 s514/.7458E15mscMoore John Dauthttp://id.loc.gov/vocabulary/relators/aut61046BOOK9910144421503321Lectures on Seiberg-Witten invariants78077UNINA