The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-manifolds

Released on by John W. Morgan
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  • The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-manifolds Book Detail

  • Author : John W. Morgan
  • Release Date : 1996
  • Publisher : Princeton University Press
  • Genre : Mathematics
  • Pages : 137
  • ISBN 13 : 0691025975
  • File Size : 16,16 MB
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The Seiberg-Witten Equations and Applications to the Topology of Smooth Four-manifolds by John W. Morgan PDF Summary

Book Description: The 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.

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Lectures on Seiberg-Witten Invariants

Lectures on Seiberg-Witten Invariants

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Riemannian, symplectic and complex geometry are often studied by means ofsolutions to systems ofnonlinear differential equations, such as the equa tions of geod

Lectures on Seiberg-Witten Invariants

Lectures on Seiberg-Witten Invariants

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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 possib

Notes on Seiberg-Witten Theory

Notes on Seiberg-Witten Theory

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After background on elliptic equations, Clifford algebras, Dirac operators, and Fredholm theory, chapters introduce solutions of the Seiberg-Witten equations an