Seibert Witten and Gromov Invariants for Symplectic 4-manifolds

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9781571460615: Seibert Witten and Gromov Invariants for Symplectic 4-manifolds
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The book contains a complete proof of the remarkable result relating the Seiberg-Witten and Gromov invariants of symplectic four manifolds. The first chapter proves that pseudo-holomorphic curves can be sonstruction from solutions to the Seiberg-Witten equations. The second chapter describes how the Gromov invariant for compact symplectic 4-manifolds assigns an integer to each dimension 2-cohomology class (or roughly speaking, counts with suitable weights, compact, pseudo-holomorphic submanifolds whose fundamental class is Poincare dual to the cohomology class in question. The third chapter continues the proof of the equivalence of Gromov invariants and the Seiberg-Witten invariants. In this chapter, a construction which associates solutions of the one-parameter family of Weiber-Witten equations to certain symplectic submanifolds in X (Pseudo-holomorphic ones.) The final chapter shows that counting for the two invariants yeilds the same answer.

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About the Author:

Clifford Henry Taubes is a senior mathematics professor at Harvard University. He has published extensively on differential geometry and related mathematical subjects.

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A brilliant proof of a significant theorem. -- reader

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Other Popular Editions of the Same Title

9781571462039: Seiberg-Witten and Gromov invariants for symplectic 4-manifolds (2010 re-issue)

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ISBN 10:  1571462031 ISBN 13:  9781571462039
Publisher: International Press of Boston, I..., 2010
Softcover

9781571460899: Seiberg-Witten and Gromov Invariants for Symplectic 4-manifolds (First International Press Lecture)

Intern..., 2005
Hardcover