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CBMS Regional Conference Series in Mathematics
1996; 366 pp; softcover
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 point-set 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.
Graduate students and research mathematicians interested in algebraic topology.
"Absolutely necessary to have this guide-book 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
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