000			02434nam a22002657a 4500
003			ISI Library, Kolkata
005			20250508124731.0
008			250421b |||||||| |||| 00| 0 eng d
020			_a9780691025971
040			_aISI Library _bEnglish
082	0	4	_223rd _a516.36 _bM847
100	1		_aMorgan, John W. _eauthor
245	1	0	_aThe Seiberg-Witten equations and applications to the topology of smooth four-manifolds/ _cJohn W. Morgan
260			_aPrinceton, N.J.: _bPrinceton University Press, _c1996
300			_avi, 128 pages; _c23 cm.
490	0		_aMathematical Notes _v44
504			_aIncludes bibliography
505	0		_aIntroduction -- Clifford Algebras and Spin Groups -- Spin Bundles and the Dirac Operator -- The Seiberg-Witten Moduli Space -- Curvature Identities and Bounds -- The Seiberg-Witten Invariant -- Invariants of Kähler Surfaces
520			_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.
650	0		_aDifferential Geometry
650	0		_aFour-manifolds (Topology)
650	0		_aSeiberg-Witten Invariants
650	0		_aMathematical Physics
942			_cBK _2ddc
999			_c436642 _d436642