Apparently (e.g. see bottom left of first column on p3 of this manuscript) the representations of $SU(2)$ can be identified with diagrams of non-intersecting curves (unoriented embedded $1$-manifolds) in a disk. This is supposedly related to the Rumer-Teller-Weyl theorem. (Context: this is of significant importance to physicist, since the latter naturally arises when considering the braiding of particles in two-dimensional space. Hence this identification would explain why $SU(2)$ Chern-Simons theories are common tools to describe so-called topological phases of matter.)
Can anyone illuminate this connection between $SU(2)$ and curves in a disk? An intuitive understanding would be ideal.
