nLab
Parametrized Homotopy Theory

Context

Homotopy theory

Stable Homotopy theory

Cohomology

cohomology

Special and general types

Special notions

Variants

Extra structure

Operations

Theorems

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 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 October 13, 2013 06:09:49 by Urs Schreiber (89.204.137.206)