Iterating the cobar construction
About this Title
Justin R. Smith
Publication: Memoirs of the American Mathematical Society
Publication Year 1994: Volume 109, Number 524
ISBNs: 978-0-8218-2588-4 (print); 978-1-4704-0101-6 (online)
MathSciNet review: 1208225
MSC: Primary 55U15; Secondary 55P35, 55R20, 57T30
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
- 1. Introduction
- 2. m-coalgebras
- 3. The bar and cobar constructions
- 4. Fibrations and twisted tensor products