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Iterating the Cobar Construction

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Iterating the Cobar Construction Synopsis

This book develops a new topological invariant called the m-structure, which incorporates all information contained in the canonical coproduct and the Steenrod operations. Given a chain complex equipped with an m-structure, Smith shows that its cobar construction also has a natural m-structure. This derived m-structure of the cobar construction corresponds to the m-structure of the loop space of the original space under the map that carries the cobar construction to the loop space. This result allows one to form iterated cobar constructions which Smith shows are homotopy equivalent to iterated loop spaces. These results are applied to the computation of the cohomology algebra structure of total spaces of fibrations.

About This Edition

ISBN: 9780821825884
Publication date:
Author: Justin R Smith
Publisher: American Mathematical Society
Format: Paperback
Pagination: 141 pages
Series: Memoirs of the American Mathematical Society
Genres: Mathematics