Foundations of Stable Homotopy Theory

A comprehensive introduction to stable homotopy theory for beginning graduate students, from motivating phenomena to current research.

David Barnes (Author), Constanze Roitzheim (Author)

9781108482783, Cambridge University Press

Hardback, published 26 March 2020

430 pages
23.4 x 15.8 x 2.7 cm, 0.7 kg

'Especially as it seems to be very carefully written, I expect that it will become a standard textbook in the field.' Julie Bergner, zbMATH

The beginning graduate student in homotopy theory is confronted with a vast literature on spectra that is scattered across books, articles and decades. There is much folklore but very few easy entry points. This comprehensive introduction to stable homotopy theory changes that. It presents the foundations of the subject together in one place for the first time, from the motivating phenomena to the modern theory, at a level suitable for those with only a first course in algebraic topology. Starting from stable homotopy groups and (co)homology theories, the authors study the most important categories of spectra and the stable homotopy category, before moving on to computational aspects and more advanced topics such as monoidal structures, localisations and chromatic homotopy theory. The appendix containing essential facts on model categories, the numerous examples and the suggestions for further reading make this a friendly introduction to an often daunting subject.

Introduction
1. Basics of stable homotopy theory
2. Sequential spectra and the stable homotopy category
3. The suspension and loop functors
4. Triangulated categories
5. Modern categories of spectra
6. Monoidal structures
7. Left Bousfield localisation
Appendix. Model categories
References
Index.

Subject Areas: Algebraic topology [PBPD]