Transformation Groups
Description
"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. Günter M. Ziegler, TU Berlin
Reviews / Votes
"There are many exercises after each section, which are a great help and were carefully chosen for pedagogical value. The mathematical community should thank the author for his efforts, and I, for one, am looking forward to his book on homotopy representations." Mathematical Reviews
More details
Other editions
Additional editions
Content
- Intro
- Chapter I Foundations
- 1. Basic notions
- 2. General remarks. Examples
- 3. Elementary properties
- 4. Functorial properties
- 5. Differentiable manifolds. Tubes and slices
- 6. Families of subgroups
- 7. Equivariant maps
- 8. Bundles
- 9. Vector bundles
- 10. Orbit categories, fundamental groups, and coverings
- 11. Elementary algebra of transformation groups
- Chapter II Algebraic Topology
- 1. Equivariant CW-complexes
- 2. Maps between complexes
- 3. Obstruction theory
- 4. The classification theorem of Hopf
- 5. Maps between complex representation spheres
- 6. Stable homotopy. Homology. Cohomology
- 7. Homology with families
- 8. The Burnside ring and stable homotopy
- 9. Bredon homology and Mackey functors
- 10. Homotopy representations
- Chapter III Localization
- 1. Equivariant bundle cohomology
- 2. Cohomology of some classifying spaces
- 3. Localization
- 4. Applications of localization
- 5. Borel-Smith functions
- 6. Further results for cyclic groups. Applications
- Chapter IV The Burnside Ring
- 1. Additive invariants
- 2. The Burnside ring
- 3. The space of subgroups
- 4. Prime ideals
- 5. Congruences
- 6. Finiteness theorems
- 7. Idempotent elements
- 8. Induction categories
- 9. Induction theory
- 10. The Burnside ring and localization
- Bibliography
- Further reading
- Subject index and symbols
- More symbols
