Axiomatic stable homotopy theory
著者
書誌事項
Axiomatic stable homotopy theory
（Memoirs of the American Mathematical Society, no. 610）
American Mathematical Society, 1997
大学図書館所蔵 件 / 全22件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
"July 1997, volume 128, number 610 (second of 4 numbers)"
Includes bibliographical references (p. 109-111) and index (p. 112-114)
内容説明・目次
内容説明
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 work: provides a reference for standard results and constructions in stable homotopy theory; discusses applications of those results to algebraic settings, such as group theory and commutative algebra; provides a unified treatment of several different situations in stable homotopy, including equivariant stable homotopy and localizations of the stable homotopy category; and, also provides a context for nilpotence and thick subcategory theorems, such as the nilpotence theorem of Devinatz-Hopkins-Smith and the thick subcategory theorem of Hopkins-Smith in stable homotopy theory, and the thick subcategory theorem of Benson-Carlson-Rickard in representation theory. 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.
目次
Introduction and definitions Smallness, limits and constructibility Bousfield localization Brown representability Nilpotence and thick subcategories Noetherian stable homotopy categories Connective stable homotopy theory Semisimple stable homotopy theory Examples of stable homotopy theory Future directions.
「Nielsen BookData」 より