Memoirs of the American Mathematical Society 1994; 141 pp; softcover Volume: 109 ISBN10: 0821825887 ISBN13: 9780821825884 List Price: US$41 Individual Members: US$24.60 Institutional Members: US$32.80 Order Code: MEMO/109/524
 This book develops a new topological invariant called the mstructure, which incorporates all information contained in the canonical coproduct and the Steenrod operations. Given a chain complex equipped with an mstructure, Smith shows that its cobar construction also has a natural mstructure. This derived mstructure of the cobar construction corresponds to the mstructure 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. Table of Contents  Introduction
 mcoalgebras
 The bar and cobar constructions
 Fibrations and twisted tensor products
 Appendices
 Bibliography
