CBMS Regional Conference Series in Mathematics 1996; 366 pp; softcover Number: 91 ISBN10: 0821803190 ISBN13: 9780821803196 List Price: US$60 Member Price: US$48 All Individuals: US$48 Order Code: CBMS/91
 This volume introduces equivariant homotopy, homology, and cohomology theory, along with various related topics in modern algebraic topology. It explains the main ideas behind some of the most striking recent advances in the subject. The book begins with a development of the equivariant algebraic topology of spaces culminating in a discussion of the Sullivan conjecture that emphasizes its relationship with classical Smith theory. It then introduces equivariant stable homotopy theory, the equivariant stable homotopy category, and the most important examples of equivariant cohomology theories. The basic machinery that is needed to make serious use of equivariant stable homotopy theory is presented next, along with discussions of the Segal conjecture and generalized Tate cohomology. Finally, the book gives an introduction to "brave new algebra", the study of pointset level algebraic structures on spectra and its equivariant applications. Emphasis is placed on equivariant complex cobordism, and related results on that topic are presented in detail. Features:  Introduces many of the fundamental ideas and concepts of modern algebraic topology.
 Presents comprehensive material not found in any other book on the subject.
 Provides a coherent overview of many areas of current interest in algebraic topology.
 Surveys a great deal of material, explaining main ideas without getting bogged down in details.
Readership Graduate students and research mathematicians interested in algebraic topology. Reviews "Absolutely necessary to have this guidebook on the desk ... applies to the advanced student as well as to the educated scientist. The presentation is clear, reliable, informative and motivating ... there is no comparable recent book in algebraic topology ... almost certainly guides further research."  Bulletin of the London Mathematical Society "The exposition and choice of topics by May and his collaborators are well crafted to bring the uninitiated up to speed in a subject that has a long technical past."  Bulletin of the AMS Table of Contents  Introduction
 Equivariant cellular and homology theory
 Postnikov systems, localization, and completion
 Equivariant rational homotopy theory
 Smith theory
 Categorical constructions; equivariant applications
 The homotopy theory of diagrams
 Equivariant bundle theory and classifying spaces
 The Sullivan conjecture
 An introduction to equivariant stable homotopy
 \(G\)CW\((V)\) complexes and \(RO(G)\)graded cohomology
 The equivariant Hurewicz and suspension theorems
 The equivariant stable homotopy category
 \(RO(G)\)graded homology and cohomology theories
 An introduction to equivariant \(K\)theory
 An introduction to equivariant cobordism
 Spectra and \(G\)spectra; change of groups; duality
 The Burnside ring
 Transfer maps in equivariant bundle theory
 Stable homotopy and Mackey functors
 The Segal conjecture
 Generalized Tate cohomology
 Twisted halfsmash products and function spectra
 Brave new algebra
 Brave new equivariant foundations
 Brave new equivariant algebra
 Localization and completion in complex bordism
 A completion theorem in complex cobordism
 Calculations in complex equivariant bordism
 Bibliography
 Index
