Stable Categories and Structured Ring Spectra
Series: Mathematical Sciences Research Institute Publications; 69;
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Product details:
- Publisher Cambridge University Press
- Date of Publication 21 July 2022
- ISBN 9781009123297
- Binding Hardback
- No. of pages442 pages
- Size 240x162x30 mm
- Weight 820 g
- Language English 280
Categories
Short description:
A graduate-level introduction to the homotopical technology in use at the forefront of modern algebraic topology.
MoreLong description:
This comprehensive text focuses on the homotopical technology in use&&&160;at the forefront of modern algebraic topology. Following on from a&&&160;standard introductory algebraic topology sequence, it will provide&&&160;students with a comprehensive background in spectra and structured&&&160;ring spectra. Each chapter is an extended tutorial by a leader in the&&&160;field, offering the first really accessible treatment of the modern&&&160;construction of the stable category in terms of both model categories&&&160;of point-set diagram spectra and infinity-categories. It is one of the&&&160;only textbook sources for operadic algebras, structured ring spectra,&&&160;and Bousfield localization, which are now basic techniques in the&&&160;field, and the book provides a rare expository treatment of spectral&&&160;algebraic geometry. Together the contributors - Emily Riehl, Daniel&&&160;Dugger, Clark Barwick, Michael A. Mandell, Birgit Richter, Tyler Lawson,&&&160;and Charles Rezk - offer a complete, authoritative source to learn the&&&160;foundations of this vibrant area.
MoreTable of Contents:
1. Introduction Andrew J. Blumberg, Teena Gerhardt, and Michael A. Hill; 2. Homotopical categories: from model categories to (&&&8734;,1)-categories Emily Riehl; 3. Stable categories and spectra via model categories Daniel Dugger; 4. Stable homotopy theory via &&&8734;-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.
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