fundamental group of complement of curve in $\mathbb{R}^4$

Question

I'm interested in the fundamental group of $\pi_1(\mathbb{R}^4-\mathcal{C})$, here $C$ a smooth curve without boundary(compact or noncompact).

I think by Alexlander duality I can see that $H_1(\mathbb{R}^4-\mathcal{C})$ is $0$, however I'm not sure about fundamental group. If I can prove the fundamental group is abelian, the problem is done, however I have no idea to show it, can anyone help me? Thanks!