STATISTICS AND SPIN ON 2-DIMENSIONAL SURFACES

The fundamental groups of the configuration spaces for the O(3) nonlinear sigma-model on the compact genus g surfaces T2g and on the connected sums R2#T2g are known for any soliton number N. So are the braid groups for N spinless particles on these manifolds. The representations of these groups govern the possible statistics of solitons and particles. We show that when spin and creation/annihilation processes are introduced, the fundamental groups for the particles are the same as the corresponding sigma-model groups. These fundamental groups incorporate the spin-statistics connection and are of greater physical relevance than the standard braid groups.