It is shown that fractional statistics on a torus are consistent only with multicomponent wave functions. This is expected to be generally true for all 2D, closed, multiply connected, orientable manifolds. The fractional quantum Hall effect with periodic boundary conditions is seen to fit into this new picture, where the quasiholes may be interpreted as a kind of generalized anyons.

• Received 16 January 1990

DOI:https://doi.org/10.1103/PhysRevLett.64.1995