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Lectures on Seiberg-Witten Invariants / Edition 2
     

Lectures on Seiberg-Witten Invariants / Edition 2

by John D. Moore, J. D. Moore
 

ISBN-10: 3540412212

ISBN-13: 9783540412212

Pub. Date: 05/18/2001

Publisher: Springer Berlin Heidelberg

This book gives a streamlined introduction to the theory of Seiberg-Witten invariants suitable for second-year graduate students. These invariants can be used to prove that there are many compact topological four-manifolds which have more than one smooth structure, and that others have no smooth structure at all. This topic provides an excellent example of how

Overview

This book gives a streamlined introduction to the theory of Seiberg-Witten invariants suitable for second-year graduate students. These invariants can be used to prove that there are many compact topological four-manifolds which have more than one smooth structure, and that others have no smooth structure at all. This topic provides an excellent example of how global analysis techniques, which have been developed to study nonlinear partial differential equations, can be applied to the solution of interesting geometrical problems. In the second edition, some material has been expanded for better comprehension.

Product Details

ISBN-13:
9783540412212
Publisher:
Springer Berlin Heidelberg
Publication date:
05/18/2001
Series:
Lecture Notes in Mathematics Series , #1629
Edition description:
2nd ed. 2001
Pages:
124
Product dimensions:
9.21(w) x 6.14(h) x 0.29(d)

Table of Contents

1. Preliminaries 1.1. Introduction 1.2. What is a vector bundle? 1.3. What is a connection? 1.4. The curvature of a connection 1.5. Characteristic classes 1.6. The Thom form 1.7. The universal bundle 1.8. Classification of connections 1.9. Hodge theory 2. Spin geometry on four-manifolds 2.1. Euclidean geometry and the spin groups 2.2. What is a spin structure? 2.3. Almost complex and spin-c structures 2.4. Clifford algebras 2.5. The spin connection 2.6. The Dirac operator 2.7. The Atiyah-Singer index theorem 3. Global analysis 3.1. The Seiberg-Witten equations 3.2. The moduli space 3.3. Compactness of the moduli space 3.4. Transversality 3.5. The intersection form 3.6. Donaldson's theorem 3.7. Seiberg-Witten invariants 3.8. Dirac operators on Kaehler surfaces 3.9. Invariants of Kaehler surfaces Bibliography Index

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