Parametrized Homotopy Theory
Paths and cylinders
Stable Homotopy theory
Special and general types
This entry collects links related to the book
- May, Sigurdsson, Parametrized Homotopy Theory, MAS Mathematical Surveys and Monographs, vol. 132, 2006 (webpage, pdf)
on parameterized stable homotopy theory, hence on stable homotopy theory in slice (infinity,1)-toposes Top for given topological base spaces : the homotopy theory of ex-spaces and parametrized spectra.
A survey is in the slides
One application is twisted cohomology: instead of cocycles given by maps , twisted cocycles are given by sections of a bundle of spectra over .
A discussion of some of these issues using tools from (infinity,1)-category theory are in
A general abstract context for parameterized spectra are tangent (infinity,1)-toposes.
Revised on January 6, 2016 17:28:46
by Urs Schreiber