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
A topological space $X$, or rather its homotopy type, is called simple if
the fundamental group $\pi_1(X)$ is abelian;
its canonical action on all higher homotopy groups $\pi_{\bullet \geq 2}(X)$ is trivial.
and thus, in particular,
every loop space is nilpotent
(since all its connected components are homotopy equivalent to the unit component, which is a connected H-space).
(See May-Ponto 12, p. 49 (77 of 542))
Simple spaces are also nilpotent spaces (May-Ponto 12, p. 49 (77 of 542)).
Created on September 15, 2020 at 14:06:51. See the history of this page for a list of all contributions to it.