Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 344 / 2 / b

Outside a defect core writeAround any closed curve on which $\mathbf{p}\ne 0$, its topological charge is the winding numberSingle-valued polar order requires $q\in \mathbb{Z}$. A nonzero value prevents the field inside the loop from being continuously deformed to a uniform nonvanishing field, so the core must contain a zero or singularity.