From path integrals to anyons

I offer a pedagogical review of the homotopy arguments for fractional statistics in two dimensions. These arguments arise naturally in path-integral language since they necessarily consider the properties of paths rather than simply permutations. The braid group replaces the permutation group as the basic structure for quantum statistics; hence properties of the braid group on several surfaces are briefly discussed. Finally, the question of multiple (real-space) occupancy is addressed; I suggest that the ''traditional'' treatment of this question (i.e., an assumption that many-anyon wavefunctions necessarily vanish for multiple occupancy) needs reexamination. (author). 19 refs, 1 fig