Parallelizable

A sphere $\Bbb{S}^n$ is parallelizable if there exist $n$ cuts containing linearly independent tangent vectors. There exist only three parallelizable spheres: $\Bbb{S}^1$, $\Bbb{S}^3$, and $\Bbb{S}^7$ (Adams 1962, Le Lionnais 1983).

See also Sphere

References

Adams, J. F. ``On the Non-Existence of Elements of Hopf Invariant One.'' Bull. Amer. Math. Soc. 64, 279-282, 1958.

Adams, J. F. ``On the Non-Existence of Elements of Hopf Invariant One.'' Ann. Math. 72, 20-104, 1960.

Le Lionnais, F. Les nombres remarquables. Paris: Hermann, p. 49, 1983.