Transformation Groups

Front Cover
Walter de Gruyter, 1987 - Mathematics - 311 pages
The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. APart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. THe works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. IN addition, it can serve as a guide for lectures and seminars on a graduate level. THe series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics.WHile the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. IN times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. IN this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. PLease submit any book proposals to Niels Jacob.
 

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Contents

Foundations
1
Basic notions
2
General remarks Examples
10
Elementary properties
22
Functorial properties
32
Differentiable manifolds Tubes and slices
38
Families of subgroups
46
Equivariant maps
50
Localization
177
Cohomology of some classifying spaces
183
Localization
190
Applications of localization
197
BorelSmith functions
210
Further results for cyclic groups Applications
218
The Burnside Ring
227
The Burnside ring
240

Bundles
54
Vector bundles
67
Orbit categories fundamental groups and coverings
72
Elementary algebra of transformation groups
77
Algebraic Topology 95 Chapter II Algebraic Topology 1 Equivariant CWcomplexes
95
Maps between complexes
104
Obstruction theory
111
The classification theorem of Hopf
122
Maps between complex representation spheres
133
Stable homotopy Homology Cohomology
139
Homology with families
150
The Burnside ring and stable homotopy
155
Bredon homology and Mackey functors
160
Homotopy representations
167
The space of subgroups
248
Prime ideals
251
Congruences
256
Finiteness theorems
260
Idempotent elements
266
Induction categories
271
Induction theory
279
The Burnside ring and localization
285
Bibliography
295
Further reading
306
Subject index and symbols
307
More symbols 312
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Page 304 - Fixed points of periodic transformations, Appendix B in S. Lefschetz, Algebraic topology, Amer.

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