Stable Categories and Structured Ring Spectra

A graduate-level introduction to the homotopical technology in use at the forefront of modern algebraic topology.

Andrew J. Blumberg (Edited by), Teena Gerhardt (Edited by), Michael A. Hill (Edited by)

9781009123297, Cambridge University Press

Hardback, published 21 July 2022

442 pages
24 x 16.2 x 3 cm, 0.82 kg

'This book serves as a comprehensive introduction to this active field of research. It is a highly beneficial resource for early-career researchers and more experienced mathematicians with different backgrounds, because it can guide the reader to the growing (and aging) literature on the subject. In particular, it fulfills the editors' goal of serving as a reference for students who have a basic knowledge of standard algebraic topology and want to learn more about spectra and structured ring spectra, thereby filling a gap in the literature.' Steen Sagave, MathSciNet

This comprehensive text focuses on the homotopical technology in use at the forefront of modern algebraic topology. Following on from a standard introductory algebraic topology sequence, it will provide students with a comprehensive background in spectra and structured ring spectra. Each chapter is an extended tutorial by a leader in the field, offering the first really accessible treatment of the modern construction of the stable category in terms of both model categories of point-set diagram spectra and infinity-categories. It is one of the only textbook sources for operadic algebras, structured ring spectra, and Bousfield localization, which are now basic techniques in the field, and the book provides a rare expository treatment of spectral algebraic geometry. Together the contributors — Emily Riehl, Daniel Dugger, Clark Barwick, Michael A. Mandell, Birgit Richter, Tyler Lawson, and Charles Rezk — offer a complete, authoritative source to learn the foundations of this vibrant area.

1. Introduction Andrew J. Blumberg, Teena Gerhardt, and Michael A. Hill
2. Homotopical categories: from model categories to (∞,1)-categories Emily Riehl
3. Stable categories and spectra via model categories Daniel Dugger
4. Stable homotopy theory via ∞-categories Clark Barwick
5. Operads and operadic algebras in homotopy theory Michael A. Mandell
6. Commutative ring spectra Birgit Richter
7. An introduction to Bousfield localization Tyler Lawson
8. Spectral algebraic geometry Charles Rezk
Bibliography
Index.