Homotopy group with coefficients

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In topology, a branch of mathematics, for i \ge 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 (G, i) to X, and is denoted by \pi_i(X; G).[1] For i \ge 3, \pi_i(X; G) is a group. Note \pi_i(X; \mathbb{Z}) are the usual homotopy groups of X.

References

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  1. Weibel 2013, Ch. IV. Definition 2.1