nLab
homotopy group with coefficients

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 generalization of the notion of homotopy groups.

Definition

Given a pointed space XX and finitely generated abelian group AA and n2n\ge2, we set

π n(X,A)[P n(A),X], \pi_n(X,A) \;\coloneqq\; [P^n(A),X] \,,

where P n(A)P^n(A) is the nnth Peterson space of AA and [,][-,-] denotes pointed homotopy classes.

References

Last revised on April 5, 2021 at 02:12:05. See the history of this page for a list of all contributions to it.