Linking Numbers, Spin, and Statistics of Solitons

The spin and statistics of solitons in the (2+1)- and (3+1)-dimensional nonlinear $\sigma$ models is considered. For the (2+1)-dimensional case, there is the possibility of fractional spin and exotic statistics; for 3+1 dimensions the usual spin-statistics relation is demonstrated. The linking-number interpretation of the Hopf invariant and the use of suspension considerably simplify the analysis.