Intrinsic quasiparticle's spin and fractional quantum Hall effect on Riemann surfaces

We derive the braid relations of the charged anyons interacting with a magnetic field on Riemann surfaces. The braid relations are used to calculate the quasiparticle's spin in the fractional quantum Hall states on Riemann surfaces. The quasiparticle's spin is found to be topological independent and satisfies physical restrictions.