Rings, Modules, and Algebras in Stable Homotopy Theory Paperback / softback
by A.D. Elmendorf, I. Kriz, M.A. Mandell, J.Peter May, M. Cole
Part of the Mathematical Surveys and Monographs series
Paperback / softback
Description
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
Information
-
Out of Stock - We are unable to provide an estimated availability date for this product
- Format:Paperback / softback
- Pages:249 pages
- Publisher:American Mathematical Society
- Publication Date:30/04/2007
- Category:
- ISBN:9780821843031
Information
-
Out of Stock - We are unable to provide an estimated availability date for this product
- Format:Paperback / softback
- Pages:249 pages
- Publisher:American Mathematical Society
- Publication Date:30/04/2007
- Category:
- ISBN:9780821843031
