stable homotopy theory
Paths and cylinders
Stable Homotopy theory
One may think of classical homotopy theory as the study of the (∞,1)-category Top of topological spaces, or rather of its homotopy category .
To every (∞,1)-category is associated its corresponding stable (∞,1)-category of spectrum objects. For Top this is the stable (∞,1)-category of spectra, . Stable homotopy theory is the study of , or rather of its homotopy category, the stable homotopy category .
A tool of major importance in stable homotopy theory and its application to higher algebra is the symmetric monoidal smash product of spectra which allows us to describe A-∞ rings and E-∞ rings as ordinary monoid objects in a model category that presents .
When the spaces and spectra in question carry an action of a group the theory refines to
An excellent general survey is
- A. Elmendorf, I. Kriz, P. May, Modern foundations for stable homotopy theory (pdf)
A survey of formalisms used in stable homotopy theory – tools to present the triangulated homotopy category of a stable (infinity,1)-category – is in
An account in terms of (∞,1)-category theory is in section 7 of
Revised on April 24, 2013 19:39:54
by Urs Schreiber