Abstract
We study bosons interacting with an abelian Chern-Simons field on Riemann surfaces of genus . It is shown that a singular gauge transformation brings the hamiltonian to free form. The transformed wave functions furnish a multi-component representation of the braid group studied by Imbo and March-Russell. The construction constitutes a proof of the equivalence of bosons coupled to a Chern-Simons field and anyons and generalizes the well known equivalence of the two pictures on the plane.
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