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Structured Ring Spectra

Part of London Mathematical Society Lecture Note Series

Editors:
Andrew Baker, University of Glasgow
Birgit Richter, Rheinische Friedrich-Wilhelms-Universität Bonn

Andrew Baker, Birgit Richter, Andrey Lazarev, Stefan Schwede, Michael Joachim, Anthony Elmendorf, Michael Mandell, Paul Goerss, Michael Hopkins, Alan Robinson, Maria Basterra

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Date Published: November 2004
availability: Available
format: Paperback
isbn: 9780521603058

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About the Authors

Within algebraic topology, the prominent role of multiplicative cohomology theories has led to a great deal of foundational research on ring spectra and in the 1990s this gave rise to significant new approaches to constructing categories of spectra and ring-like objects in them. This book contains some important new contributions to the theory of structured ring spectra as well as survey papers describing these and relationships between them. One important aspect is the study of strict multiplicative structures on spectra and the development of obstruction theories to imposing strictly associative and commutative ring structures on spectra. A different topic is the transfer of classical algebraic methods and ideas, such as Morita theory, to the world of stable homotopy.
- Provides overview papers on up to date topics in structured ring spectra
- Describes recently developed obstruction theories for multiplicative structures on ring spectra
- First book to collect recent results in the field and to compare the different approaches
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Product details
- Date Published: November 2004
- format: Paperback
- isbn: 9780521603058
- length: 240 pages
- dimensions: 228 x 152 x 15 mm
- weight: 0.342kg
- availability: Available
Table of Contents
1. The development of structured ring spectra Anthony Elmendorf
2. Compromises forced by Lewis's Theorem Anthony Elmendorf
3. Permutative categories as a model of connective stable homotopy Anthony Elmendorf and Michael Mandell
4. Morita Theory in Abelian, derived and stable model categories Stefan Schwede
5. Higher coherences in equivariant K-theory Michael Joachim
6. Co-homology theories for commutative S-algebras Maria Basterra and Birgit Richter
7. Classical obstructions and S-algebras Alan Robinson
8. Moduli spaces of commutative ring spectra Paul Goerss and Michael Hopkins
9. Cohomology theories for highly structured ring spectra Andrey Lazarev.
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Editors
Andrew Baker, University of Glasgow
Andew Baker is Reader in Mathematics at University of Glasgow. He is the author of the textbook Matrix Groups: An Introduction to Lie Group Theory, as well as numerous publications on algebraic topology, algebra and number theory in a wide range of journals and conference proceedings. He is also an editor for Glasgow Mathematical Journal and Homology and Homotopy and Applications.
Birgit Richter, Rheinische Friedrich-Wilhelms-Universität Bonn
Birgit Richter is wissenschaftlich Assistentin at Universität Bonn in Germany. He has published articles in several mathematical journals such as Mathematische Annalen,Topology, Annales de l'Institut Fourier, Journal of Pure and Applied Algebra, K-theory and Mathematical Proceedings of the Cambridge Philosophical Society.
Contributors
Andrew Baker, Birgit Richter, Andrey Lazarev, Stefan Schwede, Michael Joachim, Anthony Elmendorf, Michael Mandell, Paul Goerss, Michael Hopkins, Alan Robinson, Maria Basterra