Download EBOOK Lectures on SeibergWitten Invariants PDF for free
 
Category: Science & Geography
The author of the book: John D. Moore
Format files: PDF, EPUB, TXT, DOCX
The size of the: 233 KB
Language: English
ISBN13: 9783540412212
Edition: SpringerVerlag Berlin and Heidelberg GmbH & Co. K
Date of issue: 24 April 2001

Description of the book "Lectures on SeibergWitten Invariants":
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 infinitedimensional manifolds. A striking applications of the new technology is Donaldson's theory of "antiselfdual" connections on SU(2)bundles over fourmanifolds, which applies the YangMills equations from mathematical physics to shed light on the relationship between the classification of topological and smooth fourmanifolds. This reverses the expected direction of PDF application from topology to differential equations to mathematical physics. Even though the YangMills 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 fourmanifolds 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 YangMills equation, but can yield many of the most important results from Donaldson's theory. These are the SeibergWitte ePub~ 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 SeibergWitten approach to Donaldson theory accessible to secondyear graduate students who had already taken basic courses in differential geometry and algebraic topology.
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John D. Moore
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