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[null,"1.","Record Nr.",null,"UNISA996466535003316"]
[null,null,"Autore",null,"Moore John D"]
[null,null,"Titolo",null,"Lectures on Seiberg-Witten Invariants [[electronic resource] /] / by John D. Moore"]
[null,null,"Pubbl/distr/stampa",null,"Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2001"]
[null,null,"ISBN",null,"3-540-40952-1"]
[null,null,"Edizione",null,"[2nd ed. 2001.]"]
[null,null,"Descrizione fisica",null,"1 online resource (VIII, 121 p.)"]
[null,null,"Collana",null,"Lecture Notes in Mathematics, , 0075-8434 ; ; 1629"]
[null,null,"Classificazione",null,"58E15"]
[null,null,"Disciplina",null,"510 s"]
[{"$nulls":4},"514/.74"]
[null,null,"Soggetti",null,"Algebra"]
[{"$nulls":4},"Algebraic topology"]
[{"$nulls":4},"Calculus of variations"]
[{"$nulls":4},"Global analysis (Mathematics)"]
[{"$nulls":4},"Manifolds (Mathematics)"]
[{"$nulls":4},"System theory"]
[{"$nulls":4},"Algebraic geometry"]
[{"$nulls":4},"Algebraic Topology"]
[{"$nulls":4},"Calculus of Variations and Optimal Control; Optimization"]
[{"$nulls":4},"Global Analysis and Analysis on Manifolds"]
[{"$nulls":4},"Systems Theory, Control"]
[{"$nulls":4},"Algebraic Geometry"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Bibliographic Level Mode of Issuance: Monograph"]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,null,"Sommario/riassunto","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 "]
[{"$nulls":4},"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."]