UID:
almahu_9947366248602882
Format:
1 online resource (477 p.)
ISBN:
1-281-76325-X
,
9786611763251
,
0-08-087359-6
Series Statement:
Pure and applied mathematics, a series of monographs and textbooks ; v. 46
Content:
Introduction to compact transformation groups
Note:
Description based upon print version of record.
,
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
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7. Some Examples of O(n)-Spaces8. 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
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4. Euler Characteristics and Ranks5. 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
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10. Finiteness of Number of Orbit TypesExercises 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
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1. Functional Structures and Smooth Actions2. 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
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6. Actions on Poincaré Duality Spaces
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English
Additional Edition:
ISBN 0-12-128850-1
Language:
English
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