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Lectures on Seiberg-Witten Invariants

Door John D. Moore

Categorie	Algemeen wetenschap
Boeknummer	#341202-ZA18
Titel	Lectures on Seiberg-Witten Invariants
Auteur	Moore, John D.
Boektype	Paperback
Uitgeverij	Berlin/Heidelberg : Springer-Verlag
Jaar van uitgave	1996
ISBN10	3540614559
ISBN13	9783540614555
Taal	Engels
Beschrijving	Paperback, illustrated with numerous equations, 8vo. Lecture Notes in Mathematics 1629.
Samenvatting	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 thou... (Lees verder)gh 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.
Pagina's	105
Conditie	Goed — Small crease in top right corner of front cover, name in pen on title page.
Prijs	€ 30,00

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