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Item Details
| Title:
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RINGS, MODULES, AND ALGEBRAS IN STABLE HOMOTOPY THEORY
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| By: |
A.D. Elmendorf, I. Kriz, M.A. Mandell |
| Format: |
Paperback |
| List price:
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£113.00 |
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We believe that this item is permanently unavailable, and so we cannot source
it.
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| ISBN 10: |
0821843036 |
| ISBN 13: |
9780821843031 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
15 April, 2007 |
| Series: |
Mathematical Surveys and Monographs No. 47 |
| Pages: |
249 |
| Description: |
Introduces a fresh point-set level approach to stable homotopy theory that has had many applications and promises to have a lasting impact on the subject. Given the sphere spectrum $S$, this title constructs a smash product in a complete category of '$S$-modules' whose derived category is equivalent to the classical stable homotopy category. |
| Synopsis: |
This book introduces a new point-set level approach to stable homotopy theory that has already had many applications and promises to have a lasting impact on the subject. Given the sphere spectrum $S$, the authors construct an associative, commutative, and unital smash product in a complete and cocomplete category of ""$S$-modules"" whose derived category is equivalent to the classical stable homotopy category. This construction allows for a simple and algebraically manageable definition of ""$S$-algebras"" and ""commutative $S$-algebras"" in terms of associative, or associative and commutative, products $R\wedge SR \longrightarrow R$. These notions are essentially equivalent to the earlier notions of $A {\infty $ and $E {\infty $ ring spectra, and the older notions feed naturally into the new framework to provide plentiful examples. There is an equally simple definition of $R$-modules in terms of maps $R\wedge SM\longrightarrow M$. When $R$ is commutative, the category of $R$-modules also has a |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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