nLab
simple topological space

Contents

Context

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

A topological space XX, or rather its homotopy type, is called simple if

  1. the fundamental group π 1(X)\pi_1(X) is abelian;

  2. its canonical action on all higher homotopy groups π 2(X)\pi_{\bullet \geq 2}(X) is trivial.

Examples

and thus, in particular,

(See May-Ponto 12, p. 49 (77 of 542))

Properties

Simple spaces are also nilpotent spaces (May-Ponto 12, p. 49 (77 of 542)).

References

Created on September 15, 2020 at 10:06:51. See the history of this page for a list of all contributions to it.