LEADER 04744nam 22007935 450 001 9910144421503321 005 20210913155339.0 010 $a3-540-40952-1 024 7 $a10.1007/978-3-540-40952-6 035 $a(CKB)1000000000575758 035 $a(SSID)ssj0000324391 035 $a(PQKBManifestationID)12072490 035 $a(PQKBTitleCode)TC0000324391 035 $a(PQKBWorkID)10314190 035 $a(PQKB)10728420 035 $a(DE-He213)978-3-540-40952-6 035 $a(MiAaPQ)EBC3087227 035 $a(PPN)155201840 035 $a(EXLCZ)991000000000575758 100 $a20121227d2001 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aLectures on Seiberg-Witten Invariants /$fby John D. Moore 205 $a2nd ed. 2001. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2001. 215 $a1 online resource (VIII, 121 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1629 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-41221-2 320 $aIncludes bibliographical references and index. 330 $aRiemannian, symplectic and complex geometry are often studied by means ofsolutions to systems ofnonlinear differential equations, such as the equa­ tions of geodesics, minimal surfaces, pseudoholomorphic curves and Yang­ Mills connections. For studying such equations, a new unified technology has been developed, involving analysis on infinite-dimensional manifolds. A striking applications of the new technology is Donaldson's theory of "anti-self-dual" connections on SU(2)-bundles over four-manifolds, which applies the Yang-Mills equations from mathematical physics to shed light on the relationship between the classification of topological and smooth four-manifolds. This reverses the expected direction of application from topology to differential equations to mathematical physics. Even though the Yang-Mills equations are only mildly nonlinear, a prodigious amount of nonlinear analysis is necessary to fully understand the properties of the space of solutions. . At our present state of knowledge, understanding smooth structures on topological four-manifolds seems to require nonlinear as opposed to linear PDE's. It is therefore quite surprising that there is a set of PDE's which are even less nonlinear than the Yang-Mills equation, but can yield many of the most important results from Donaldson's theory. These are the Seiberg-Witte~ equations. These lecture notes stem from a graduate course given at the University of California in Santa Barbara during the spring quarter of 1995. The objective was to make the Seiberg-Witten approach to Donaldson theory accessible to second-year graduate students who had already taken basic courses in differential geometry and algebraic topology. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1629 606 $aAlgebra 606 $aAlgebraic topology 606 $aCalculus of variations 606 $aGlobal analysis (Mathematics) 606 $aManifolds (Mathematics) 606 $aSystem theory 606 $aGeometry, Algebraic 606 $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000 606 $aAlgebraic Topology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28019 606 $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016 606 $aGlobal Analysis and Analysis on Manifolds$3https://scigraph.springernature.com/ontologies/product-market-codes/M12082 606 $aSystems Theory, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/M13070 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 615 0$aAlgebra. 615 0$aAlgebraic topology. 615 0$aCalculus of variations. 615 0$aGlobal analysis (Mathematics) 615 0$aManifolds (Mathematics) 615 0$aSystem theory. 615 0$aGeometry, Algebraic. 615 14$aAlgebra. 615 24$aAlgebraic Topology. 615 24$aCalculus of Variations and Optimal Control; Optimization. 615 24$aGlobal Analysis and Analysis on Manifolds. 615 24$aSystems Theory, Control. 615 24$aAlgebraic Geometry. 676 $a510 s 676 $a514/.74 686 $a58E15$2msc 700 $aMoore$b John D$4aut$4http://id.loc.gov/vocabulary/relators/aut$061046 906 $aBOOK 912 $a9910144421503321 996 $aLectures on Seiberg-Witten invariants$978077 997 $aUNINA