SPINNING PARTICLES, BRAID-GROUPS AND SOLITONS

We develop general techniques for computing the fundamental group of t he configuration space of n identical particles, possessing a generic internal structure, moving on a manifold M. This group generalizes the n-string braid group of M which is the relevant object for structurel ess particles. In particular, we compute these generalized braid group s for particles with an internal spin degree of freedom on an arbitrar y M. A study of their unitary representations allows us to determine t he available spectrum of spin and statistics on M in a certain class o f quantum theories. One interesting result is that half-integral spin quantizations are obtained on certain manifolds having an obstruction to an ordinary spin structure. We also compare our results to correspo nding ones for topological solitons in O(d + 1)-invariant nonlinear si gma models in d + 1 dimensions, generalizing recent studies in two spa tial dimensions. Finally, we prove that there exists a general scalar quantum theory yielding half-integral spin for particles (or O(d + 1) solitons) on a closed, orientable manifold M if and only if M possesse s a spin, structure.