The suspension homomorphism $\sigma :\pi_{n+k}(S^n)\to \pi_{n+k+l}(S^{n+l})$ is an isomorphism for $n\gt k+1$.

In this statement, one can replace $S^n$ with any $(n-1)$-connected space$Y$ while replacing $S^{n+l}$ with the corresponding suspension $\Sigma^{l} Y$.

This theorem justifies introducing the stable homotopy groups of spheres$\pi_k(S):=\pi_{n+k}(S^n)$, as well as stable homotopy groups $\pi_k^S(Y) = \pi_{n+k}(\Sigma^n Y)$, both independent of $n$ where $n\gt k+1$.