Homotopy group with coefficients

In topology, a branch of mathematics, for ${\displaystyle i\geq 2}$, the i-th homotopy group with coefficients in an abelian group G of a based space X is the pointed set of homotopy classes of based maps from the Moore space of type ${\displaystyle (G,i)}$ to X, and is denoted by ${\displaystyle \pi _{i}(X;G)}$.[1] For ${\displaystyle i\geq 3}$, ${\displaystyle \pi _{i}(X;G)}$ is a group. Note that ${\displaystyle \pi _{i}(X;\mathbb {Z} )}$ are the usual homotopy groups of X.

References

1. Weibel 2013, Ch. IV. Definition 2.1

• Weibel, Charles (2013). "The K-book: An introduction to algebraic K-theory".