Cohomological Methods in Transformation Groups
Published on 1. July 1993
Book
Hardback
484 pages
978-0-521-35022-8 (ISBN)
Description
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.
Reviews / Votes
"...a clear, beautifully written presentation of some of the central developments in topology in the last thirty-odd years, centering on a subject which we dare predict will never cease to surprise, namely, the action of groups on topological spaces. May it be the forerunner of several other such expositions." Gian-Carlo Rota, The Bulletin of Mathematical Books "...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 SocietyMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Dimensions
Height: 235 mm
Width: 157 mm
Thickness: 33 mm
Weight
930 gr
ISBN-13
978-0-521-35022-8 (9780521350228)
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Schweitzer Classification
Persons
Content
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 Poincare duality spaces; Appendices; References; Indexes.