Relative homotopy group

Summary

The relative homotopy group $\pi_n(X, A, x_0)$ of a pair $A \subseteq X$ consists of homotopy classes of maps of an $n$-disk into $X$ with boundary in $A$. It is the homotopy analogue of relative homology. The relative groups fit into a long exact sequence with the homotopy groups of $A$ and of $X$. This sequence is the main tool for computing homotopy groups of fibrations.