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(E–pub Free) [Modern Classical Homotopy Theory] BY Jeffrey Strom

Riodicity ocalization 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 To the expert read as terse proofs; to novices they are challenges that draw them in and help them to Thoroughly Understand The Argumen. understand the argumen.

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Modern Classical Homotopy Theory

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The core of classical homotopy is a body OF AND THEOREMS THAT EMERGED IN THE 1950S ideas and theorems that emerged in the 1950s was Different Class laterargely codified in the notion of a model category This core includes the notions of fibration and cofibration; CW complexes; ong fiber and cofiber seuences; oop 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 imits and colimits by the theory of model categories and that homotopy imits and colimits central roles The exposition is guided by the principle that it is generally preferable to prove topological results using topology than algebra The anguage and basic theory of imits and colimits make it possible to penetrate deep into the subject with just the rudiments of algebra of homotopy Socialist Realism limits and colimits make it possible to penetrate deep into the subject with just the rudiments of algebra text does reach advanced territory including the Steenrod algebra Bott pe.