Cover

Half-title

Title

Copyright

Dedication

Contents

Preface

Introduction

1 The Klein correspondence

1.1 Projective space and Grassmannian manifolds

1.2 Twistor manifolds and correspondences

1.3 The Plucker embedding of M into P5

1.4 The linear geometry of the Klein quadric

1.5 Group actions and homogeneous structures

1.6 Minkowski and Euclidean space

2 Fiber bundles

2.1 Vector bundles and principal bundles

2.2 Differential forms

2.3 Tensor and spinor bundles

2.4 Connections and curvature

3 The algebraic topology of manifolds and bundles

3.1 Homotopy and homology

3.2 Sheaf theory

3.3 Sheaf cohomology

3.4 Characteristic classes

3.5 Clifford algebras and spin bundles

3.6 Spectral sequences

4 Linear field theories

4.1 The wave equation and Maxwell's equations

4.2 Spinors and spinor fields

4.3 The action principle and interactions

4.4 Poincare and conformal invariance

5 Gauge theory

5.1 The essentials of gauge theory

5.2 Yang-Mills instantons

5.3 Magnetic poles

6 General relativity

6.1 Space-time, spinors, and Einstein's equations

6.2 Self-duality and gravitational instantons

7 Massless free fields

7.1 Holomorphic solutions of the

7.2 The linear Penrose transform

7.3 Integral formulas for massless fields

7.4 Hyperfunetion solutions of the

8 Self-dual gauge fields

8.1 Correspondence between self-dual gauge fields and holomorphic bundles

8.2 Ansatze for SU(2)-fields

8.3 The twistor construction of instantons

8.4 Magnetic poles: solutions

9 Twistors for self-dual space-time

9.1 Correspondence between self-dual space-times and curved twistor spaces

9.2 Constructing self-dual space-times

10 The Penrose transform for general gauge fields

10.1 The Penrose transformation on formal neighborhoods

10.2 Supergeometry and Yang-Mills fields

References

Subject and author index