CLASSICAL TOPOLOGY AND QUANTUM STATISTICS

We review the theory of statistics of identical systems in terms of the properties of the classical configuration space. Special emphasis is placed on the influence of the connectivity of this space on quantum statistics. The theory shows that exotic statistical systems, such as those obeying fractional statistics, can occur in all dimensions. Particle statistics in one dimension involves novel features particular to this dimension and these are briefly described. The proof of a topological spin-statistics theorem which avoids field theory or relativity is also outlined.