Structured Ring Spectra

This book contains some important new contributions to the theory of structured ring spectra.

Andrew Baker (Edited by), Birgit Richter (Edited by)

9780521603058, Cambridge University Press

Paperback, published 18 November 2004

240 pages
22.8 x 15.2 x 1.5 cm, 0.342 kg

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.

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.

Subject Areas: Algebraic topology [PBPD]