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100   $a20140829h19961996  uy             0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 14$aThe Seiberg-Witten equations and applications to the topology of smooth four-manifolds /$fJohn W. Morgan
210  1$aPrinceton, New Jersey :$cPrinceton University Press,$d1996.
210  4$d©1996
215   $a1 online resource (138 p.)
225 1 $aMathematical Notes ;$v44
300   $aDescription based upon print version of record.
311   $a1-322-06334-6 
311   $a0-691-02597-5 
320   $aIncludes bibliographical references.
327   $tFront matter --$tContents --$t1. Introduction --$t2. Clifford Algebras and Spin Groups --$t3. Spin Bundles and the Dirac Operator --$t4. The Seiberg-Witten Moduli Space --$t5. Curvature Identities and Bounds --$t6. The Seiberg-Witten Invariant --$t7. Invariants of Kahler Surfaces --$tBibliography
330   $aThe recent introduction of the Seiberg-Witten invariants of smooth four-manifolds has revolutionized the study of those manifolds. The invariants are gauge-theoretic in nature and are close cousins of the much-studied SU(2)-invariants defined over fifteen years ago by Donaldson. On a practical level, the new invariants have proved to be more powerful and have led to a vast generalization of earlier results. This book is an introduction to the Seiberg-Witten invariants. The work begins with a review of the classical material on Spin c structures and their associated Dirac operators. Next comes a discussion of the Seiberg-Witten equations, which is set in the context of nonlinear elliptic operators on an appropriate infinite dimensional space of configurations. It is demonstrated that the space of solutions to these equations, called the Seiberg-Witten moduli space, is finite dimensional, and its dimension is then computed. In contrast to the SU(2)-case, the Seiberg-Witten moduli spaces are shown to be compact. The Seiberg-Witten invariant is then essentially the homology class in the space of configurations represented by the Seiberg-Witten moduli space. The last chapter gives a flavor for the applications of these new invariants by computing the invariants for most Kahler surfaces and then deriving some basic toological consequences for these surfaces.
410  0$aMathematical notes (Princeton University Press) ;$v44.
606   $aFour-manifolds (Topology)
606   $aSeiberg-Witten invariants
606   $aMathematical physics
610   $aAffine space.
610   $aAffine transformation.
610   $aAlgebra bundle.
610   $aAlgebraic surface.
610   $aAlmost complex manifold.
610   $aAutomorphism.
610   $aBanach space.
610   $aClifford algebra.
610   $aCohomology.
610   $aCokernel.
610   $aComplex dimension.
610   $aComplex manifold.
610   $aComplex plane.
610   $aComplex projective space.
610   $aComplex vector bundle.
610   $aComplexification (Lie group).
610   $aComputation.
610   $aConfiguration space.
610   $aConjugate transpose.
610   $aCovariant derivative.
610   $aCurvature form.
610   $aCurvature.
610   $aDifferentiable manifold.
610   $aDifferential topology.
610   $aDimension (vector space).
610   $aDirac equation.
610   $aDirac operator.
610   $aDivision algebra.
610   $aDonaldson theory.
610   $aDuality (mathematics).
610   $aEigenvalues and eigenvectors.
610   $aElliptic operator.
610   $aElliptic surface.
610   $aEquation.
610   $aFiber bundle.
610   $aFrenet?Serret formulas.
610   $aGauge fixing.
610   $aGauge theory.
610   $aGaussian curvature.
610   $aGeometry.
610   $aGroup homomorphism.
610   $aHilbert space.
610   $aHodge index theorem.
610   $aHomology (mathematics).
610   $aHomotopy.
610   $aIdentity (mathematics).
610   $aImplicit function theorem.
610   $aIntersection form (4-manifold).
610   $aInverse function theorem.
610   $aIsomorphism class.
610   $aK3 surface.
610   $aKähler manifold.
610   $aLevi-Civita connection.
610   $aLie algebra.
610   $aLine bundle.
610   $aLinear map.
610   $aLinear space (geometry).
610   $aLinearization.
610   $aManifold.
610   $aMathematical induction.
610   $aModuli space.
610   $aMultiplication theorem.
610   $aNeighbourhood (mathematics).
610   $aOne-form.
610   $aOpen set.
610   $aOrientability.
610   $aOrthonormal basis.
610   $aParameter space.
610   $aParametric equation.
610   $aParity (mathematics).
610   $aPartial derivative.
610   $aPrincipal bundle.
610   $aProjection (linear algebra).
610   $aPullback (category theory).
610   $aQuadratic form.
610   $aQuaternion algebra.
610   $aQuotient space (topology).
610   $aRiemann surface.
610   $aRiemannian manifold.
610   $aSard's theorem.
610   $aSign (mathematics).
610   $aSobolev space.
610   $aSpin group.
610   $aSpin representation.
610   $aSpin structure.
610   $aSpinor field.
610   $aSubgroup.
610   $aSubmanifold.
610   $aSurjective function.
610   $aSymplectic geometry.
610   $aSymplectic manifold.
610   $aTangent bundle.
610   $aTangent space.
610   $aTensor product.
610   $aTheorem.
610   $aThree-dimensional space (mathematics).
610   $aTrace (linear algebra).
610   $aTransversality (mathematics).
610   $aTwo-form.
610   $aZariski tangent space.
615  0$aFour-manifolds (Topology)
615  0$aSeiberg-Witten invariants.
615  0$aMathematical physics.
676   $a514/.2
700   $aMorgan$b John W.$f1946-$057422
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910828604403321
996   $aSeiberg-Witten equations and applications to the topology of Smooth four-manifolds$9923773
997   $aUNINA