**Memoirs of the American Mathematical Society**

1994;
141 pp;
Softcover

MSC: Primary 55;

Print ISBN: 978-0-8218-2588-4

Product Code: MEMO/109/524

List Price: $44.00

Individual Member Price: $26.40

**Electronic ISBN: 978-1-4704-0101-6
Product Code: MEMO/109/524.E**

List Price: $44.00

Individual Member Price: $26.40

# Iterating the Cobar Construction

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*Justin R. Smith*

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.

#### Readership

Researchers in algebraic topology.