
eBook ISBN: | 978-1-4704-0101-6 |
Product Code: | MEMO/109/524.E |
List Price: | $44.00 |
MAA Member Price: | $39.60 |
AMS Member Price: | $26.40 |

eBook ISBN: | 978-1-4704-0101-6 |
Product Code: | MEMO/109/524.E |
List Price: | $44.00 |
MAA Member Price: | $39.60 |
AMS Member Price: | $26.40 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 109; 1994; 141 ppMSC: Primary 55
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.
ReadershipResearchers in algebraic topology.
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Table of Contents
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Chapters
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1. Introduction
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2. m-coalgebras
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3. The bar and cobar constructions
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4. Fibrations and twisted tensor products
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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.
-
Chapters
-
1. Introduction
-
2. m-coalgebras
-
3. The bar and cobar constructions
-
4. Fibrations and twisted tensor products