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Iterating the Cobar Construction
 
Iterating the Cobar Construction
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
Iterating the Cobar Construction
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Iterating the Cobar Construction
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
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1091994; 141 pp
    MSC: 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.

    Readership

    Researchers in algebraic topology.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. m-coalgebras
    • 3. The bar and cobar constructions
    • 4. Fibrations and twisted tensor products
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1091994; 141 pp
MSC: 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.

Readership

Researchers in algebraic topology.

  • Chapters
  • 1. Introduction
  • 2. m-coalgebras
  • 3. The bar and cobar constructions
  • 4. Fibrations and twisted tensor products
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.