  We show that the number of distinct topological states associated to a given
knotted defect, $L$, in a nematic liquid crystal is equal to the determinant of
the link $L$. We give an interpretation of these states, demonstrate how they
may be identified in experiments and describe the consequences for material
behaviour and interactions between multiple knots. We show that stable knots
can be created in a bulk cholesteric and illustrate the topology by classifying
a simulated Hopf link. In addition we give a topological heuristic for the
resolution of strand crossings in defect coarsening processes which allows us
to distinguish topological classes of a given link and to make predictions
about defect crossings in nematic liquid crystals.
