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Memoirs of the American Mathematical Society
1997; 114 pp; softcover
List Price: US$47
Individual Members: US$28.20
Institutional Members: US$37.60
Order Code: MEMO/128/610
This book gives an axiomatic presentation of stable homotopy theory. It starts with axioms defining a "stable homotopy category"; using these axioms, one can make various constructions--cellular towers, Bousfield localization, and Brown representability, to name a few. Much of the book is devoted to these constructions and to the study of the global structure of stable homotopy categories.
Next, a number of examples of such categories are presented. Some of these arise in topology (the ordinary stable homotopy category of spectra, categories of equivariant spectra, and Bousfield localizations of these), and others in algebra (coming from the representation theory of groups or of Lie algebras, as well as the derived category of a commutative ring). Hence one can apply many of the tools of stable homotopy theory to these algebraic situations.
This book presents stable homotopy theory as a branch of mathematics in its own right with applications in other fields of mathematics. It is a first step toward making stable homotopy theory a tool useful in many disciplines of mathematics.
Graduate students and research mathematicians interested in algebraic topology, representation theory, and algebraic geometry.
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