Freudenthal suspension theorem

This fact is related to: homotopy groups

Statement

Let $X$ be a $(n-1)$-connected space having a nondegenerate basepoint $x_0$. Then the suspension homomorphism from ${\pi }_q(X)\to {\pi }_{q+1}(\mathrm{\Sigma }X)$ is an isomorphism for $q\le 2n-2$ and is surjective for $q=2n-1$.