《塞伯格-威顿方程及其在光滑四流形拓扑中的应用》由(美)摩根著，是Seiberg—Witten的入门书籍。近年来，光滑四流形Seiberg—Witten不变量的引入是流形研究的革新。不变量的本质是规范理论，这和十五年前Donaldson定义的已经得到深入研究的SU（2）—不变量属同一脉息。实际上，这个新的不变量被证明了更加强大，将早起的研究成果引入到一个更广泛的平台。读者对象：数学专业的高年级本科生、研究生和相关的科研人员。

1 Introduction

2 Clifford Algebras and Spin Groups

 2.1 The Clifford Algebras

 2.2 The groups Pin(V) and Spin(V)

 2.3 Splitting of the Clifford Algebra

 2.4 The complexification of the Cl(V)

 2.5 The Complex Spin Representation

 2.6 The Group Spine(V)

3 Spin Bundles and the Dirac Operator

 3.1 Spin Bundles and Clifford Bundles

 3.2 Connections and Curvature

 3.3 The Dirac Operator

 3.4 The Case of Complex Manifolds

4 The Seiberg-Witten Moduli Space

 4.1 The Equations

 4.2 Space of Configurations

 4.3 Group of Changes of Gauge

 4.4 The Action

 4.5 The Quotient Space

 4.6 The Elliptic Complex

5 Curvature Identities and Bounds

 5.1 Curvature Identities

 5.2 A Priori bounds

 5.3 The Compactness of the Moduli Space

6 The Seiberg-Witten Invariant

 6.1 The Statement

 6.2 The Parametrized Moduli Space

 6.3 Reducible Solutions

 6.4 Compactness of the Perturbed Moduli Space

 6.5 Variation of the Metric and Self-dual Two-form

 6.6 Orientability of the Moduli Space

 6.7 The Case when b+2 (X) > 1

 6.8 An Involution in the Theory

 6.9 The Case when b+(X) = 1

7 Invariants of K~hler Surfaces

 7.1 The Equations over a Kahler Manifold

 7.2 Holomorphic Description of the Moduli Space

 7.3 Evaluation for K/ihler Surfaces

 7.4 Computation for K/ihler Surfaces

 7.5 Final Remarks

Bibliography