AMS Bookstore LOGO amslogo
Return to List

AMS TextbooksAMS Applications-related Books

Modern Classical Homotopy Theory
Jeffrey Strom, Western Michigan University, Kalamazoo, MI
cover
SEARCH THIS BOOK:

Graduate Studies in Mathematics
2011; 835 pp; hardcover
Volume: 127
ISBN-10: 0-8218-5286-8
ISBN-13: 978-0-8218-5286-6
List Price: US$95
Member Price: US$76
Order Code: GSM/127
[Add Item]

Request Permissions

See also:

Lecture Notes in Algebraic Topology - James F Davis and Paul Kirk

Differential Algebraic Topology: From Stratifolds to Exotic Spheres - Matthias Kreck

Mapping Degree Theory - Enrique Outerelo and Jesus M Ruiz

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 participate in research at (part of) the current frontier of homotopy theory. Proofs are not provided outright. Rather, they are presented in the form of directed problem sets. To the expert, these read as terse proofs; to novices they are challenges that draw them in and help them to thoroughly understand the arguments.

Request an examination or desk copy.

Readership

Graduate students and research mathematicians interested in algebraic topology and homotopy theory.

Powered by MathJax

  AMS Home | Comments: webmaster@ams.org
© Copyright 2014, American Mathematical Society
Privacy Statement

AMS Social

AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia