The idea that topologically protected quantum states, such as anyons, may be attached to super/semiconductor heterostructures has received enormous attention, but experimental signatures in 1D systems remain elusive. Here we revisit theoretical underpinnings of anyons in 2D fractional quantum Hall (FQH) systems, whose signatures have been experimentally observed by independent groups. We highlight novel theorems about the hopfion or $\mathbb {C}P^{1}\text{-model}$ , understood as quantization of FQH surplus flux in 2-cohomotopy, which retrodicts Abelian FQH anyon properties in fine detail. Examining this theoretical model further, we find that islands of expelled flux enlarge the ground-state monodromy from an Abelian group to a (framed spherical) braid group, non-Abelian for two or more islands, so that non-Abelian anyonic states become topologically admissible; superconducting islands are one candidate realization of such flux expulsion.