Multisheet configuration space and fractional quantum statistics

We show that if one uses a multisheet configuration space for a system of identical particles, then fractional quantum statistics in two dimensions can be geometrically characterized as a topological quantum number for going from one sheet to the next. Furthermore, the spectrum of such a g-sheet system is shown to consist of the spectra of all species of anyons obeying different fractional statistics 0 = 2rrp/q (p=0,1, . . .,q - 1) with the same denominator q. A lattice computation has been done to verify this. Various aspects of the multisheet formalism are discussed.