# 0708-1300/Homework Assignment 8

Just one problem. Let $K$ be a knot in ${\mathbb R}^3$ presented by a planar diagram $D$. With a massive use of Van-Kampen's theorem, show that the fundamental group of the complement of $K$ has a presentation (the "Wirtinger" presentation) with one generator for each edge of $D$ and two relations for each crossing of $D$, as indicated in the figure below.