# What does it mean by “combing a sphere”?

Here $M$ is a smooth manifold and $V(M)$ is the space of vector fields on $M$, $V^*(M)$ is the space of covector fields on $M$ and $T_{(q,r)}(M)$ is the space of $(q,r)$ tensor fields on $M$. What does it mean the example in picture? Namely, what does it mean by impossible to comb a sphere? Could anyone please explain?

• As a side note, this is completely wrong that a vector field on $S^2$ must vanish at least at two points, it is only one point. For the construction of a vector field on $S^2$ with only one zero, see here. – C. Falcon Apr 24 '18 at 14:43