# Homotopy group

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Homotopy groups are tools used in algebraic topology to classify topological spaces. The different ways to map an n-sphere continuously into a given topological space are divided into equivalence classes, called homotopy classes. The set of homotopy classes of maps of the n-sphere into a space may be endowed with a group structure by a means analogous to the concatenation operation used to construct the fundamental group; this group is usually denoted πn. However, as long as $n \geq 2$, the homotopy groups πn(X) are abelian groups.