For $P=\{y=x^2,z=0\}$, I need to prove that $\mathbb{R}^3 \backslash P$ is not simply connected by showing that there exists $\alpha$ such that $\int_S \alpha \neq 0$ for the circle $\{y^2+z^2=1,x=0 \}$.
My attempt is to use $$\alpha = \frac{zdy-ydz}{z^2+y^2}$$ but to do this I need to find a diffeomorphism that transforms the parabola defined by $P$ to the line $y=0$. This is where I'm stuck.
Please help!