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Bibliographic Details
Main Authors:	Petrie, Ted (Author), Randall, John D. (Author)
Format:	Book
Language:	English
Published:	New York u.a. Dekker 1984
Series:	Pure and applied mathematics 82
Subjects:	Groupes topologiques de transformation Variétés (Mathématiques) Manifolds (Mathematics) Topological transformation groups Topologische Transformationsgruppe Transformationsgruppe Mannigfaltigkeit
Links:	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
Physical Description:	VII, 266 S.
ISBN:	0824771567

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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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isbn	0824771567
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series	Pure and applied mathematics
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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
volume_link	(DE-604)BV000001885
work_keys_str_mv	AT petrieted transformationgroupsonmanifolds AT randalljohnd transformationgroupsonmanifolds

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Call Number:	0102 MAT 578f 2001 A 27429 Floor plan
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