Cohomological Methods in Transformation Groups

The reader with a relatively modest background in algebraic topology can penetrate rather deeply into the subject.

Christopher Allday (Author), Volker Puppe (Author)

9780521350228, Cambridge University Press

Hardback, published 1 July 1993

484 pages
22.9 x 15.2 x 3.2 cm, 0.88 kg

"...written in a lucid and careful style. All the areas previously mentioned are discussed (as well as many more), paying special attention to the key elements involved in the proofs. Alternate approaches are often discussed, and many interesting examples are provided. The authors have done an admirable job of explaining this area of mathematics. Thoughtful remarks are included in several places, there are exercises at the end of each chapter, and the references are abundant. Moreover, there are two appendices which provide much of the necessary background in commutative and differential algebra....[I]t should prove useful to a broad spectrum of mathematicians." Alejandro Adem, Bulletin of the American Mathematical Society

This is an account of the theory of certain types of compact transformation groups, namely those that are susceptible to study using ordinary cohomology theory and rational homotopy theory, which in practice means the torus groups and elementary abelian p-groups. The efforts of many mathematicians have combined to bring a depth of understanding to this area. However to make it reasonably accessible to a wide audience, the authors have streamlined the presentation, referring the reader to the literature for purely technical results and working in a simplified setting where possible. In this way the reader with a relatively modest background in algebraic topology and homology theory can penetrate rather deeply into the subject, whilst the book at the same time makes a useful reference for the more specialised reader.

Preface
1. Equivalent cohomology of G-CW-complexes and the Borel construction
2. Summary of some aspects of rational homotopy theory
3. Localisation
4. General results on torus and p-torus actions
5. Actions on Poincaré duality spaces
Appendices
References
Indexes.

Subject Areas: Groups & group theory [PBG]