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Lectures On Seiberg-witten Invariants (lecture Notes In Mathematics) 🔍
John Douglas Moore (auth.) Springer-Verlag Berlin Heidelberg, Lecture Notes in Mathematics 1629, 2, 2001
英语 [en] · DJVU · 0.6MB · 2001 · 📘 非小说类图书 · 🚀/duxiu/lgli/lgrs/scihub/upload/zlib · Save
描述
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.
备用文件名
lgli/dvd61/Moore J.D. - Lectures on Seiberg-Witten Invariants(1996)(105).djvu
备用文件名
lgrsnf/dvd61/Moore J.D. - Lectures on Seiberg-Witten Invariants(1996)(105).djvu
备用文件名
scihub/10.1007/978-3-540-40952-6.pdf
备用文件名
zlib/Mathematics/John Douglas Moore (auth.)/Lectures on Seiberg-Witten Invariants_497231.djvu
备用出版商
Springer Berlin Heidelberg : Imprint : Springer
备用出版商
Springer Spektrum. in Springer-Verlag GmbH
备用出版商
Steinkopff. in Springer-Verlag GmbH
备用版本
Lecture notes in mathematics,, 1629, Lecture notes in mathematics (Springer-Verlag) ;, 1629., Berlin, New York, New York State, 1996
备用版本
Lecture Notes in Mathematics, 1629, Berlin, Heidelberg, 1996
备用版本
Springer Nature, Berlin, Heidelberg, 2006
备用版本
Germany, Germany
元数据中的注释
mexmat -- 61
元数据中的注释
lg949415
元数据中的注释
Includes bibliographical references (p. [101]-103) and index.
备用描述
This book gives a streamlined introduction to the theory of Seiberg-Witten invariants suitable for second-year graduate students. These invariants can be used to prove that there are many compact topological four-manifolds which have more than one smooth structure, and that others have no smooth structure at all. This topic provides an excellent example of how global analysis techniques, which have been developed to study nonlinear partial differential equations, can be applied to the solution of interesting geometrical problems. In the second edition, some material has been expanded for better comprehension.
备用描述
In The Fall Of 1994, Edward Witten Proposed A Set Of Equations Which Give The Main Results Of Donaldson Theory In A Far Simpler Way Than Had Been Thought Possible. The Purpose Of These Notes Is To Provide An Elementary Introduction To The Equations That Witten Proposed. They Are Directed Towards Graduate Students Who Have Already Taken A Basic Course In Differential Geometry And Topology. John D. Moore. Includes Bibliographical References And Index.
备用描述
In 1994, Edward Witten proposed a set of equations which gave the main results of Donaldson theory in simplified way. The purpose of these notes is to provide an elementary introduction to the equations that Witten proposed. They are intended for graduate students.
备用描述
Front Matter....Pages i-viii
Preliminaries....Pages 1-44
Spin geometry on four-manifolds....Pages 45-72
Global analysis of the Seiberg-Witten equations....Pages 73-116
Back Matter....Pages 117-121
开源日期
2009-07-20
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