Transformation groups on manifolds:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Dekker
1984
|
| Series: | Pure and applied mathematics
82 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VII, 266 S. |
| ISBN: | 0824771567 |
Staff View
MARC
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| 245 | 1 | 0 | |a Transformation groups on manifolds |c Ted Petrie ; John D. Randall |
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| 300 | |a VII, 266 S. | ||
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| 490 | 1 | |a Pure and applied mathematics |v 82 | |
| 650 | 4 | |a Groupes topologiques de transformation | |
| 650 | 4 | |a Variétés (Mathématiques) | |
| 650 | 4 | |a Manifolds (Mathematics) | |
| 650 | 4 | |a Topological transformation groups | |
| 650 | 0 | 7 | |a Topologische Transformationsgruppe |0 (DE-588)4738313-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Transformationsgruppe |0 (DE-588)4127386-2 |2 gnd |9 rswk-swf |
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Record in the Search Index
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| adam_text | Contents
PREFACE m
CHAPTER 1: INTRODUCTION 1
Representations and G Spaces 1
Vector Bundles 4
Geometric Invariants of Group Actions 8
Statement of the Problem 9
Representation Theory 12
VectG(X) 18
The Grothendieck Group 20
K° x) 21
JG(X) 25
VectG(x,D, KG(X,D, JG(X,D 29
Equivariant Riemannian Metrics 31
Constructions on G Spaces 35
G Fibre Homotopy Equivalence 38
CHAPTER 2: EQUIVARIANT K THEORY 43
Introduction 43
Definition of KG 43
v
vi Contents
Cohomological Properties of K 47
The Thorn Isomorphism Theorem and the
Bott Periodicity Theorem 50
The Index 53
The Localization Theorem and Calculation
of the Index 55
The Signature 62
The Smith Problem: Semifree Actions 66
Actions of Cyclic Groups of Odd Order 70
Groups of 2 Power Order 72
CHAPTER 3: EQUIVARIANT SURGERY 74
Introduction 74
The Basics of Equivariant Surgery 80
Adding Cells and Handles 83
Motivation for Bundle Isomorphisms in Surgery 91
Definition of Equivariant Surgery 95
Handle Subtraction and Surgery 102
Elementary Properties of the Surgery Kernels 107
The Foundational Theorems of Equivariant Surgery 113
Extending Bundle Isomorphisms 126
Surgery is Possible 139
Constructing Normal Maps 153
Wall s Surgery Obstruction Groups and
Equivariant Surgery 166
Surgery to a Pseudoequivalence 179
Localization and Theorem 13.1 187
CHAPTER 4: SMITH EQUIVALENCE OF REPRESENTATIONS 193
Introduction 193
Generalities for G Vector Bundles 202
Equivariant Surgery 208
The Equivariant Signature and s Smith
Equivalence 214
Ker T,T vs. Ker res,, 224
V n
Contents va
The Kernel of the Equivariant J Homomorphism 231
Explicit Conditions for s Smith Equivalence 239
REFERENCES 249
INDEX 255
|
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| dewey-ones | 514 - Topology |
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| dewey-search | 514/.3 |
| dewey-sort | 3514 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV000238732 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:10:54Z |
| institution | BVB |
| isbn | 0824771567 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000143292 |
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| physical | VII, 266 S. |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Petrie, Ted Verfasser aut Transformation groups on manifolds Ted Petrie ; John D. Randall New York u.a. Dekker 1984 VII, 266 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 82 Groupes topologiques de transformation Variétés (Mathématiques) Manifolds (Mathematics) Topological transformation groups Topologische Transformationsgruppe (DE-588)4738313-6 gnd rswk-swf Transformationsgruppe (DE-588)4127386-2 gnd rswk-swf Mannigfaltigkeit (DE-588)4037379-4 gnd rswk-swf Topologische Transformationsgruppe (DE-588)4738313-6 s Mannigfaltigkeit (DE-588)4037379-4 s DE-604 Transformationsgruppe (DE-588)4127386-2 s Randall, John D. Verfasser aut Pure and applied mathematics 82 (DE-604)BV000001885 82 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000143292&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Petrie, Ted Randall, John D. Transformation groups on manifolds Pure and applied mathematics Groupes topologiques de transformation Variétés (Mathématiques) Manifolds (Mathematics) Topological transformation groups Topologische Transformationsgruppe (DE-588)4738313-6 gnd Transformationsgruppe (DE-588)4127386-2 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd |
| subject_GND | (DE-588)4738313-6 (DE-588)4127386-2 (DE-588)4037379-4 |
| title | Transformation groups on manifolds |
| title_auth | Transformation groups on manifolds |
| title_exact_search | Transformation groups on manifolds |
| title_full | Transformation groups on manifolds Ted Petrie ; John D. Randall |
| title_fullStr | Transformation groups on manifolds Ted Petrie ; John D. Randall |
| title_full_unstemmed | Transformation groups on manifolds Ted Petrie ; John D. Randall |
| title_short | Transformation groups on manifolds |
| title_sort | transformation groups on manifolds |
| topic | Groupes topologiques de transformation Variétés (Mathématiques) Manifolds (Mathematics) Topological transformation groups Topologische Transformationsgruppe (DE-588)4738313-6 gnd Transformationsgruppe (DE-588)4127386-2 gnd Mannigfaltigkeit (DE-588)4037379-4 gnd |
| topic_facet | Groupes topologiques de transformation Variétés (Mathématiques) Manifolds (Mathematics) Topological transformation groups Topologische Transformationsgruppe Transformationsgruppe Mannigfaltigkeit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000143292&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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