ANYONS ON HIGHER-GENUS SURFACES - A CONSTRUCTIVE APPROACH

We reconsider the problem of anyons on higher genus surfaces by embedd ing them in three-dimensional space. From a concrete realization based on three-dimensional flux tubes bound to charges moving on the surfac e, we explicitly derive all the representations of the spinning braid group. The component structure of the wave functions arises from windi ng the flux tubes around the handles. We also argue that the anyons in our construction must fulfil the generalized spin-statistics relation .