Editing Homotopy group (section)

== Related notions ==
The homotopy groups are fundamental to [[homotopy theory]], which in turn stimulated the development of [[Model category|model categories]]. It is possible to define abstract homotopy groups for [[simplicial set]]s.

[[Homology group]]s are similar to homotopy groups in that they can represent "holes" in a topological space. However, homotopy groups are often very complex and hard to compute. In contrast, homology groups are commutative (as are the higher homotopy groups). Given a topological space <math>X,</math> its ''n''th homotopy group is denoted by <math>\pi_n(X),</math> and its ''n''th homology group is denoted by <math>H_n(X)</math> or <math>H_n(X;\Z).</math>