Let $i:S^2 \to \mathbb{R}^3$ be inclusion. Let $\omega=dz$ be a 1-form on $\mathbb{R}^3$. I want to compute $i^* \omega$ and it vainishes exactly two points.
Is it right that $i^* \omega=i^*dz=d(i^*z)=d(z \circ i)$? Why does it vanishes at two points?