Equivariant stable homotopy theory
This book is a foundational piece of work in stable homotopy theory and in the theory of transformation groups. It may be roughly divided into two parts. The first part deals with foundations of (equivariant) stable homotopy theory. A workable category of CW-spectra is developed. The foundations are such that an action of a compact Lie group is considered throughout, and spectra allow desuspension by arbitrary representations. But even if the reader forgets about group actions, he will find man…
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- Full title :Equivariant stable homotopy theory / L.G. Lewis, Jr., J.P. May, M. Steinberger.
Summary
This book is a foundational piece of work in stable homotopy theory and in the theory of transformation groups. It may be roughly divided into two parts. The first part deals with foundations of (equivariant) stable homotopy theory. A workable category of CW-spectra is developed. The foundations are such that an action of a compact Lie group is considered throughout, and spectra allow desuspension by arbitrary representations. But even if the reader forgets about group actions, he will find many details of the theory worked out for the first time. More subtle constructions like smash products, function spectra, change of group isomorphisms, fixed point and orbit spectra are treated. While it is impossible to survey properly the material which is covered in the book, it does boast these general features: (i) a thorough and reliable presentation of the foundations of the theory; (ii) a large number of basic results, principal applications, and fundamental techniques presented for the first time in a coherent theory, unifying numerous treatments of special cases in the literature.
Read More ↓Edition Statements
- Publication Date:©1986.
Publication Statements
- Publisher(s):Springer-Verlag
- Place of Publication:Berlin
- Language:eng
- Publication Date:©1986.
The Physical Object
- Description:1 online resource (ix, 538 pages) : : illustrations
Edition Identifiers
- ISBN:9783540470779, 3540470778
- oclc:ocn289091362
- LC Classification:QA3
- Dewey Decimal:510
Table of Contents
Preamble : A polemical introduction to the stable category -- The equivariant stable category -- Change of universe, smash products, and change of groups -- Equivariant duality theory -- Equivariant transfer -- The Burnside ring and splittings in equivariant homology theory -- Twisted half smash products and extended powers -- Operad ring spectra -- The homological analysis of extended powers -- Thom spectra -- Equivariant Thom spectra.
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