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Iterating the Cobar Construction
Justin R. Smith

Memoirs of the American Mathematical Society
1994; 141 pp; softcover
Volume: 109
ISBN-10: 0-8218-2588-7
ISBN-13: 978-0-8218-2588-4
List Price: US$44
Individual Members: US$26.40
Institutional Members: US$35.20
Order Code: MEMO/109/524
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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.


Researchers in algebraic topology.

Table of Contents

  • Introduction
  • m-coalgebras
  • The bar and cobar constructions
  • Fibrations and twisted tensor products
  • Appendices
  • Bibliography
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