Lectures on Seiberg-Witten Invariants [[electronic resource] /] / by John D. Moore

• Autore: Moore John D
• Pubblicazione: Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2001
• Edizione: 2nd ed. 2001.
• Descrizione fisica: 1 online resource (VIII, 121 p.)
• Disciplina: 510 s; 514/.74
• Soggetto topico: Algebra; Algebraic topology; Calculus of variations; Global analysis (Mathematics); Manifolds (Mathematics); System theory; Algebraic geometry; Algebraic Topology; Calculus of Variations and Optimal Control; Optimization; Global Analysis and Analysis on Manifolds; Systems Theory, Control; Algebraic Geometry
• Classificazione: 58E15
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references and index.
• 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 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.
• Titolo autorizzato: Lectures on Seiberg-Witten invariants
• ISBN: 3-540-40952-1
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910144421503321
• Lo trovi qui: Univ. Federico II
• Serie: Lecture Notes in Mathematics, . 0075-8434 ; ; 1629