Relative Hurewicz theorem (${\pi }_r(X,A)\cong H_r(X,A;\mathbb{Z})$)

If $X$ and $A$ are simply connected and the pair is $(r-1)$-connected, with $r\ge 3$, its first possible nonzero relative homotopy group maps isomorphically to relative integral homology. This lets a basis of a free relative homology group be realized by attaching disks.