Homotopy group with coefficients

In topology, a branch of mathematics, for [math]\displaystyle{ i \ge 2 }[/math], 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 [math]\displaystyle{ (G, i) }[/math] to X, and is denoted by [math]\displaystyle{ \pi_i(X; G) }[/math]. For [math]\displaystyle{ i \ge 3 }[/math], [math]\displaystyle{ \pi_i(X; G) }[/math] is a group. The groups [math]\displaystyle{ \pi_i(X; \Z) }[/math] are the usual homotopy groups of X.

References

• Weibel, Charles (2013). "The K-book: An introduction to algebraic K-theory". http://www.math.rutgers.edu/~weibel/Kbook.html. 

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