In topology, a branch of mathematics, for
, 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
to ''X'', and is denoted by
.
For
,
is a group. The groups
are the usual
homotopy group
In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental group, denoted \pi_1(X), which records information about loops in a space. Intuitively, homotop ...
s of ''X''.
References
*
Algebraic topology
Homotopy theory
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ko:호모토피 군#계수가 있는 호모토피