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Modern Classical Homotopy Theory (Graduate Studies in Mathematics) (Graduate Studies in Mathematics, 127) by Jeffrey Strom is a nonfiction available to read on EtoBox.

What is Modern Classical Homotopy Theory (Graduate Studies in Mathematics) (Graduate Studies in Mathematics, 127) about?

The core of classical homotopy theory is a body of ideas and theorems that emerged in the 1950s and was later largely codified in the notion of a model category. This core includes the notions of fibration and cofibration; CW complexes; long fiber and cofiber sequences; loop spaces and suspensions; and so on. Brown's representability theorems show that homology and cohomology are also contained in classical homotopy theory. This text develops classical homotopy theory from a modern point of view, meaning that the exposition is informed by the theory of model categories and that homotopy limits and colimits play central roles. The exposition is guided by the principle that it is generally preferable to prove topological results using topology (rather than algebra). The language and basic theory of homotopy limits and colimits make it possible to penetrate deep into the subject with just the rudiments of algebra. The text does reach advanced territory, including the Steenrod algebra, Bott periodicity, localization, the Exponent Theorem of Cohen, Moore, and Neisendorfer, and Miller's Theorem on the Sullivan Conjecture. Thus the reader is given the tools needed to understand and partic

Who reads Modern Classical Homotopy Theory (Graduate Studies in Mathematics) (Graduate Studies in Mathematics, 127)?

Author

Jeffrey Strom

Publisher

American Mathematical Society

Published

2011

Language

EN

ISBN

9781470471637

Category

nonfiction

Subjects

Mathematics, Stem

Updated

2026-03-24