Introduction to Compact Transformation Groups
Published on 29. September 1972
458 pages
978-0-08-087359-6 (ISBN)
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Introduction to Compact Transformation Groups
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Glen E. Bredon
Introduction to Compact Transformation Groups
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01/1972
Academic Press
€94.24
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Content
- Front Cover
- Introduction to Compact Transformation Groups
- Copyright Page
- CONTENTS
- Preface
- Acknowledgments
- Chapter 0. Background on Topological Groups and Lie Groups
- 1. Elementary Properties of Topological Groups
- 2. The Classical Groups
- 3. Integration on Compact Groups
- 4. Characteristic Functions on Compact Groups
- 5. Lie Groups
- 6. The Structure of Compact Lie Groups
- Chapter I. Transformation Groups
- 1. Group Actions
- 2. Equivariant Maps and Isotropy Groups
- 3. Orbits and Orbit Spaces
- 4. Homogeneous Spaces and Orbit Types
- 5. Fixed Points
- 6. Elementary Constructions
- 7. Some Examples of O(n)-Spaces
- 8. Two Further Examples
- 9. Covering Actions
- Exercises for Chapter I
- Chapter II. General Theory of G-Spaces
- 1. Fiber Bundles
- 2. Twisted Products and Associated Bundles
- 3. Twisted Products with a Compact Group
- 4. Tubes and Slices
- 5. Existence of Tubes
- 6. Path Lifting
- 7. The Covering Homotopy Theorem
- 8. Conical Orbit Structures
- 9. Classification of G-Spaces
- 10. Linear Embedding of G-Spaces
- Exercises for Chapter II
- Chapter III. Homological Theory of Finite Group Actions
- 1. Simplicial Actions
- 2. The Transfer
- 3. Transformations of Prime Period
- 4. Euler Characteristics and Ranks
- 5. Homology Spheres and Disks
- 6. G-Coverings and Cech Theory
- 7. Finite Group Actions on General Spaces
- 8. Groups Acting Freely on Spheres
- 9. Newman's Theorem
- 10. Toral Actions
- Exercises for Chapter III
- Chapter IV. Locally Smooth Actions on Manifolds
- 1. Locally Smooth Actions
- 2. Fixed Point Sets of Maps of Prime Period
- 3. Principal Orbits
- 4. The Manifold Part of M*
- 5. Reduction to Finite Principal Isotropy Groups
- 6 . Actions on Sn with One Orbit Type
- 7. Components of B U E
- 8. Actions with Orbits of Codimension 1 or 2
- 9. Actions on Tori
- 10. Finiteness of Number of Orbit Types
- Exercises for Chapter IV
- Chapter V. Actions with Few Orbit Types
- 1. The Equivariant Collaring Theorem
- 2. The Complementary Dimension Theorem
- 3. Reduction of Structure Groups
- 4. The Straightening Lemma and the Tube Theorem
- 5. Classification of Actions with Two Orbit Types
- 6. The Second Classification Theorem
- 7. Classification of Self-Equivalences
- 8. Equivariant Plumbing
- 9. Actions on Brieskorn Varieties
- 10. Actions with Three Orbit Types
- 11. Knot Manifolds
- Exercises for Chapter V
- Chapter VI. Smooth Actions
- 1. Functional Structures and Smooth Actions
- 2. Tubular Neighborhoods
- 3. Integration of Isotopies
- 4. Equivariant Smooth Embeddings and Approximations
- 5. Functional Structures on Certain Orbit Spaces
- 6. Special G-Manifolds
- 7. Smooth Knot Manifolds
- 8. Groups of Involutions
- 9. Semifree Circle Group Actions
- 10. Representations at Fixed Points
- 11. Refinements Using Real K-Theory
- Exercises for Chapter VI
- Chapter VII. Cohomology Structure of Fixed Point Sets
- 1. Preliminaries
- 2. Some Inequalities
- 3. Zp- Actions on Projective Spaces
- 4. Some Examples
- 5. Circle Actions on Projective Spaces
- 6. Actions on Poincaré Duality Spaces
- 7. A Theorem on Involutions
- 8. Involutions on Sn × Sm
- 9. Zp- Actions on Sn × Sm
- 10. Circle Actions on a Product of Odd-Dimensional Spheres
- 11. An Application to Equivariant Maps
- Exercises for Chapter VII
- References
- Author Index
- Subject Index
- Pure and Applied Mathematics
