Lectures on Seiberg-Witten Invariants / by John Douglas Moore
(Lecture Notes in Mathematics ; 1629)
| データ種別 | 電子ブック |
|---|---|
| 版 | Second Edition |
| 出版者 | Berlin, Heidelberg : Springer Berlin Heidelberg |
| 出版年 | 2001 |
| 本文言語 | 英語 |
| 大きさ | VIII, 121 p : online resource |
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| 一般注記 | 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 |
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| 著者標目 | *Moore, John Douglas author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Algebra LCSH:Algebraic geometry LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:System theory LCSH:Calculus of variations LCSH:Algebraic topology FREE:Mathematics FREE:Algebra FREE:Algebraic Topology FREE:Calculus of Variations and Optimal Control; Optimization FREE:Global Analysis and Analysis on Manifolds FREE:Systems Theory, Control FREE:Algebraic Geometry |
| 分 類 | DC23:512 |
| 巻冊次 | ISBN:9783540409526 
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| ISBN | 9783540409526 |
| URL | http://dx.doi.org/10.1007/978-3-540-40952-6 |
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