Rational homotopy groups of a sphere
= Rational homotopy groups of a sphere
For an odd-dimensional sphere $S^{2m+1}$, only $\pi_{2m+1}(S^{2m+1})\otimes\mathbb Q$ is nonzero. For an even-dimensional sphere $S^{2m}$, the nonzero rational homotopy groups occur in degrees $2m$ and $4m-1$, and both are isomorphic to $\mathbb Q$.