In the large and thriving field of compact transformation groups an important role has long been played by cohomological methods. This book aims to give a contemporary account of such methods, in particular the applications of ordinary cohomology theory and rational homotopy theory with principal emphasis on actions of tori and elementary abelian p-groups on finite-dimensional spaces. For example, spectral sequences are not used in Chapter 1, where the approach is by means of cochain complexes; and much of the basic theory of cochain complexes needed for this chapter is outlined in an appendix. For simplicity, emphasis is put on G-CW-complexes; the refinements needed to treat more general finite-dimensional (or finitistic) G-spaces are often discussed separately. Subsequent chapters give systematic treatments of the Localization Theorem, applications of rational homotopy theory, equivariant Tate cohomology and actions on Poincaré duality spaces. Many shorter and more specialized topics are included also. Chapter 2 contains a summary of the main definitions and results from Sullivan's version of rational homotopy theory which are used in the book.
"synopsis" may belong to another edition of this title.
To make the book accessible 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 new reader can penetrate rather deeply into the subject, whilst the book at the same time makes a useful reference for the more specialised reader.Review:
"...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 Society
"About this title" may belong to another edition of this title.
Book Description Cambridge University Press, 2017. Hardcover. Book Condition: New. This item is printed on demand. Bookseller Inventory # P110521350220
Book Description Cambridge University Press. Hardcover. Book Condition: New. 0521350220 New Condition. Bookseller Inventory # NEW6.0275533
Book Description Cambridge University Press, 2016. Paperback. Book Condition: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Bookseller Inventory # ria9780521350228_lsuk
Book Description Cambridge University Press, 1993. HRD. Book Condition: New. New Book.Shipped from US within 10 to 14 business days.THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Bookseller Inventory # IP-9780521350228
Book Description Cambridge University Press, 1993. Hardcover. Book Condition: New. Bookseller Inventory # DADAX0521350220
Book Description Cambridge Univ Pr, 1993. Hardcover. Book Condition: Brand New. 482 pages. 9.25x6.25x1.00 inches. In Stock. Bookseller Inventory # __0521350220
Book Description Cambridge University Press, 1993. Hardcover. Book Condition: New. Bookseller Inventory # SONG0521350220
Book Description Cambridge University Press, 1993. HRD. Book Condition: New. New Book. Delivered from our US warehouse in 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND.Established seller since 2000. Bookseller Inventory # IP-9780521350228
Book Description 1993. Hardback. Book Condition: NEW. 9780521350228 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Bookseller Inventory # HTANDREE0454457
Book Description Cambridge University Press, 1993. Hardcover. Book Condition: New. book. Bookseller Inventory # 0521350220