In Libgober's paper [Alexander polynomial of plane algebraic curves and cyclic multiple planes][1], Example 2 (p.850), Libgober claims that the complement to this curve (i.e. $x^2u=y^3$ relative to the line in infinity $u=0$) is a retract of the complement of the trefoil knot in $S^3$. I wonder how to see this. Is in general the complement of a plane curve (relative to a line in infinity) the retract of a knot in $S^3$? If not, when is that true?

I heard that the complement to an affine curve retracts on a complement to a knot (for any weighted homogenous curve). Is that true and is there a reference?

http://homepages.math.uic.edu/~libgober/otherpapers/export/1982alexanderduke.pdf