Parametrized Homotopy Theory


Homotopy theory

Stable Homotopy theory



Special and general types

Special notions


Extra structure



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/X/X for given topological base spaces XX: 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 XAX \to A, twisted cocycles are given by sections XPX \to P of a bundle PXP \to X of spectra over XX.

A discussion of some of these issues using tools from (infinity,1)-category theory are in

See also

A general abstract context for parameterized spectra are tangent (infinity,1)-toposes.

category: reference

Revised on January 6, 2016 17:28:46 by Urs Schreiber (