04402nam 22008415 450 991014442150332120250724090705.03-540-40952-110.1007/978-3-540-40952-6(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,1617-9692 ;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,1617-9692 ;1629AlgebraAlgebraic topologyMathematical optimizationCalculus of variationsGlobal analysis (Mathematics)Manifolds (Mathematics)System theoryControl theoryGeometry, AlgebraicAlgebraAlgebraic TopologyCalculus of Variations and OptimizationGlobal Analysis and Analysis on ManifoldsSystems Theory, ControlAlgebraic GeometryAlgebra.Algebraic topology.Mathematical optimization.Calculus of variations.Global analysis (Mathematics)Manifolds (Mathematics)System theory.Control theory.Geometry, Algebraic.Algebra.Algebraic Topology.Calculus of Variations and 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