Stable Categories and Structured Ring Spectra

"The modern era in homotopy theory began in the 1960s with the profound realization, first codified by Boardman in his construction of the stable category, that the category of spaces up to stable homotopy equivalence is equipped with a rich algebraic structure, formally similar to the derived category of a commutative ring R. For example, for pointed spaces the natural map from the categorical co-product to the categorical product becomes more and more connected as the pieces themselves become more and more connected"--

List of contents

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.

About the author

Andrew J. Blumberg is Herbert and Florence Irving Professor of Cancer Data Research and Professor of Mathematics and Computer Science at Columbia University, New York.Teena Gerhardt is an associate professor in the Department of Mathematics at Michigan State University.Michael A. Hill is Professor of Mathematics at the University of California, Los Angeles.

Product details

• Authors: Andrew J. (Columbia University Blumberg
• Assisted by: Andrew J. Blumberg (Editor), Andrew J. (Columbia University Blumberg (Editor), Teena Gerhardt (Editor), Teena (Michigan State University) Gerhardt (Editor), Michael A. Hill (Editor), Michael A. (University of California Hill (Editor), Hill Michael A. (Editor)
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 30.06.2022
• EAN: 9781009123297
• ISBN: 978-1-0-0912329-7
• No. of pages: 450
• Series: Mathematical Sciences Research Institute Publications
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Miscellaneous; MATHEMATICS / Topology, Algebraic Topology