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020 _a9783540409526
_9978-3-540-40952-6
024 7 _a10.1007/978-3-540-40952-6
_2doi
050 4 _aQA150-272
072 7 _aPBF
_2bicssc
072 7 _aMAT002000
_2bisacsh
072 7 _aPBF
_2thema
082 0 4 _a512
_223
100 1 _aMoore, John Douglas.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aLectures on Seiberg-Witten Invariants
_h[electronic resource] /
_cby John Douglas Moore.
250 _aSecond Edition.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2001.
300 _aVIII, 121 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1629
520 _aRiemannian, 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.
650 0 _aAlgebra.
650 0 _aAlgebraic topology.
650 0 _aMathematical optimization.
650 0 _aGlobal analysis.
650 0 _aSystems theory.
650 0 _aGeometry, algebraic.
650 1 4 _aAlgebra.
_0http://scigraph.springernature.com/things/product-market-codes/M11000
650 2 4 _aAlgebraic Topology.
_0http://scigraph.springernature.com/things/product-market-codes/M28019
650 2 4 _aCalculus of Variations and Optimal Control; Optimization.
_0http://scigraph.springernature.com/things/product-market-codes/M26016
650 2 4 _aGlobal Analysis and Analysis on Manifolds.
_0http://scigraph.springernature.com/things/product-market-codes/M12082
650 2 4 _aSystems Theory, Control.
_0http://scigraph.springernature.com/things/product-market-codes/M13070
650 2 4 _aAlgebraic Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M11019
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662208557
776 0 8 _iPrinted edition:
_z9783540412212
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1629
856 4 0 _uhttps://doi.org/10.1007/978-3-540-40952-6
912 _aZDB-2-SMA
912 _aZDB-2-LNM
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999 _c10139
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