Introduction to compact transformation groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Acad. Press
1972
|
| Schriftenreihe: | Pure and applied mathematics
46 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI,459 S. |
| ISBN: | 0121288501 |
Internformat
MARC
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| 100 | 1 | |a Bredon, Glen E. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to compact transformation groups |
| 264 | 1 | |a New York [u.a.] |b Acad. Press |c 1972 | |
| 300 | |a XI,459 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Pure and applied mathematics |v 46 | |
| 650 | 4 | |a Lie, Groupes de | |
| 650 | 4 | |a Transformations, Groupes de | |
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Datensatz im Suchindex
| _version_ | 1804117399206625280 |
|---|---|
| adam_text | CONTENTS
Preface ix
Acknowledgments xiii
Chapter 0 Background on Topologicai Groups and Lie
Groups
1. Elementary Properties of Topologicai Groups 1
2. The Classical Groups 5
3. Integration on Compact Groups 11
4. Characteristic Functions on Compact Groups 15
5. Lie Groups 21
6. The Structure of Compact Lie Groups 26
Chapter I Transformation Groups
1. Group Actions 32
2. Equivariant Maps and Isotropy Groups 35
3. Orbits and Orbit Spaces 37
4. Homogeneous Spaces and Orbit Types 40
5. Fixed Points 44
6. Elementary Constructions 46
7. Some Examples of O(n) Spaces 49
8. Two Further Examples 55
9. Covering Actions 62
Exercises for Chapter I 67
Chapter II General Theory of G Spaces
1. Fiber Bundles 70
2. Twisted Products and Associated Bundles 72
3. Twisted Products with a Compact Group 79
4. Tubes and Slices 82
5. Existence of Tubes 84
6. Path Lifting 90
v
VI CONTENTS
7. The Covering Homotopy Theorem 92
8. Conical Orbit Structures 98
9. Classification of G Spaces 104
10. Linear Embedding of G Spaces 110
Exercises for Chapter II 112
Chapter III Homological Theory of Finite Group Actions
1. Simplicial Actions 114
2. The Transfer 118
3. Transformations of Prime Period 122
4. Euler Characteristics and Ranks 126
5. Homology Spheres and Disks 129
6. G Coverings and Cech Theory 132
7. Finite Group Actions on General Spaces 141
8. Groups Acting Freely on Spheres 148
9. Newman s Theorem 154
10. Toral Actions 158
Exercises for Chapter III 166
Chapter IV Locally Smooth Actions on Manifolds
1. Locally Smooth Actions 170
2. Fixed Point Sets of Maps of Prime Period 175
3. Principal Orbits 179
4. The Manifold Part of M* 186
5. Reduction to Finite Principal Isotropy Groups 190
6. Actions on S with One Orbit Type 196
7. Components of B u E 200
8. Actions with Orbits of Codimension 1 or 2 205
9. Actions on Tori 214
10. Finiteness of Number of Orbit Types 218
Exercises for Chapter IV 222
Chapter V Actions with Few Orbit Types
1. The Equivariant Collaring Theorem 224
2. The Complementary Dimension Theorem 230
3. Reduction of Structure Groups 233
4. The Straightening Lemma and the Tube Theorem 238
5. Classification of Actions with Two Orbit Types 246
6. The Second Classification Theorem 253
7. Classification of Self Equivalences 261
8. Equivariant Plumbing 267
CONTENTS Vli
9. Actions on Brieskorn Varieties 272
10. Actions with Three Orbit Types 280
11. Knot Manifolds 287
Exercises for Chapter V 293
Chapter VI Smooth Actions
1. Functional Structures and Smooth Actions 296
2. Tubular Neighborhoods 303
3. Integration of Isotopies 312
4. Equivariant Smooth Embeddings and Approximations 314
5. Functional Structures on Certain Orbit Spaces 319
6. Special G Manifolds 326
7. Smooth Knot Manifolds 333
8. Groups of Involutions 337
9. Semifree Circle Group Actions 347
10. Representations at Fixed Points 352
11. Refinements Using Real AVTheory 359
Exercises for Chapter VI 366
Chapter VII Cohomology Structure of Fixed Point Sets
1. Preliminaries 369
2. Some Inequalities 375
3. Z,, Actions on Projective Spaces 378
4. Some Examples 388
5. Circle Actions on Projective Spaces 393
6. Actions on Poincare Duality Spaces 400
7. A Theorem on Involutions 405
8. Involutions on S x S 410
9. Zp Actions on S x Sm 416
10. Circle Actions on a Product of Odd Dimensional Spheres 422
11. An Application to Equivariant Maps 425
Exercises for Chapter VII 428
References 432
Author Index 454
Subject Index 457
|
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| id | DE-604.BV003111677 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:53:47Z |
| institution | BVB |
| isbn | 0121288501 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001951183 |
| oclc_num | 448052 |
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| physical | XI,459 S. |
| psigel | TUB-nvmb |
| publishDate | 1972 |
| publishDateSearch | 1972 |
| publishDateSort | 1972 |
| publisher | Acad. Press |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Bredon, Glen E. Verfasser aut Introduction to compact transformation groups New York [u.a.] Acad. Press 1972 XI,459 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 46 Lie, Groupes de Transformations, Groupes de Lie groups Transformation groups Kompakte Transformationsgruppe (DE-588)4135659-7 gnd rswk-swf Kompakte Transformationsgruppe (DE-588)4135659-7 s DE-604 Pure and applied mathematics 46 (DE-604)BV010177228 46 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001951183&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bredon, Glen E. Introduction to compact transformation groups Pure and applied mathematics Lie, Groupes de Transformations, Groupes de Lie groups Transformation groups Kompakte Transformationsgruppe (DE-588)4135659-7 gnd |
| subject_GND | (DE-588)4135659-7 |
| title | Introduction to compact transformation groups |
| title_auth | Introduction to compact transformation groups |
| title_exact_search | Introduction to compact transformation groups |
| title_full | Introduction to compact transformation groups |
| title_fullStr | Introduction to compact transformation groups |
| title_full_unstemmed | Introduction to compact transformation groups |
| title_short | Introduction to compact transformation groups |
| title_sort | introduction to compact transformation groups |
| topic | Lie, Groupes de Transformations, Groupes de Lie groups Transformation groups Kompakte Transformationsgruppe (DE-588)4135659-7 gnd |
| topic_facet | Lie, Groupes de Transformations, Groupes de Lie groups Transformation groups Kompakte Transformationsgruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001951183&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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