Transformation Groups, Volume 8

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Walter de Gruyter, 1987 - Mathematics - 311 pages
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“This book is a jewel†– it explains important, useful and deep topics in Algebraic Topology that you won’t find elsewhere, carefully and in detail.”
Prof. G nter M. Ziegler, TU Berlin

 

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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
Maps between complexes
104
Obstruction theory lll
109
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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