Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 141 / 1 / c / Solution

The Alexander numbering of the three lobe regions is one and that of the central region is two, relative to the unbounded region numbered zero. Equivalently, abelianizing the three relators givesThus $A=B=C$ and $D=2A$. The class $A$ is the positively oriented meridian of a knot, so