Holmstrom Stable homotopy theory

Slides of Strickland

Some reference for stable homotopy theory in the sense of algebraic topology:

Basic

• A historical survey by May
• The blue book of Adams
• LNM0003 by Adams, looks very nice and easy to read
• See various things on the webpage of Strickland
• Many nice things are in these notes by Dundas
• D. Puppe, On the formal structure of stable homotopy theory, in Colloq. Alg. Topology, Aarhus University (1962), 65-71.
• LNM0165 Cohen 1970
• Various survey articles in Handbook of AT, in Alg Top folder

Advanced

• Ravenel: Nilpotence and Periodicity in Stable Homotopy Theory
• Morava: Towards a fundamental groupoid…

Some research articles

• http://front.math.ucdavis.edu/0907.0730 Symmetric powers in stable homotopy categories from arXiv Front: math.AG by Sergey Gorchinskiy, Vladimir Guletskii We construct Z-coefficient symmetric powers in a symmetric monoidal triangulated category, provided it is the homotopy category of a closed simplicial symmetric monoidal model category. Under certain natural assumptions, we show an existence of functorial towers for symmetric powers in distinguished triangles whose cones can be computed by Kuenneth’s rule. Our theory is applicable to the topological and motivic stable homotopy categories through the idea of symmetric spectra. Some applications are presented and open questions are raised in both topological and motivic settings.

nLab page on Stable homotopy theory