nLab
topological homotopy theory

Context

Topology

topology (point-set topology, point-free topology)

see also differential topology, algebraic topology, functional analysis and topological homotopy theory

Introduction

Basic concepts

Universal constructions

Extra stuff, structure, properties

Examples

Basic statements

Theorems

Analysis Theorems

topological homotopy theory

Homotopy theory

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology

Introductions

Definitions

Paths and cylinders

Homotopy groups

Basic facts

Theorems

Contents

Idea

Topological homotopy theory is homotopy theory for or modeled on topological spaces (in contrast to simplicial homotopy theory or localic homotopy theory).

The key tools are the Strøm model category and the classical model structure on topological spaces on the category Top of all topological spaces, or on some convenient category of topological spaces.

Revised on July 1, 2017 11:15:37 by Urs Schreiber (88.77.226.246)