Contents
Introduction xiii
Chapter 1. Preliminaries 1
§1.1. Bundles, connections and characteristic classes 1
1.1.1. Vector bundles and connections 1
1.1.2. Chern-Weil theory 12
§1.2. Basic facts about elliptic equations 16
§1.3. Clifford algebras and Dirac operators 27
1.3.1. Clifford algebras and their representations 27
1.3.2. The Spin and
Spinc
groups 34
1.3.3. Spin and
spinc
structures 40
1.3.4. Dirac operators associated to spin and
spin0
structures 46
§1.4. Complex differential geometry 53
1.4.1. Elementary complex differential geometry 54
1.4.2. Cauchy-Riemann operators 68
1.4.3. Dirac operators on almost Kahler manifolds 80
§1.5. Fredholm theory 85
1.5.1. Continuous families of elliptic operators 85
1.5.2. Genericity results 100
Chapter 2. The Seiberg-Witten Invariants 103
§2.1. Seiberg-Witten monopoles 103
IX
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