Now I have just read about how to compute $\pi_1(\mathbb{R}^3-K)$ where $K$ is the trefoil knot. Now I think I understand all the argument and in the end using van Kampen we get that that it's $\langle x,y :x^2=y^3\rangle$. Now my problem is that when I actually look at it and try to visualize what the generators are and what $x^2$ and $y^3$ are I can't see to understand why we have that these would be homotopic. Does anyone know a reference with the geometric indeas behind this and some pictures concerning this ?
Thanks in advance