  In this paper I discuss how the component structure of anyon wave functions
arises in theories with non-relativistic matter coupled to a Chern-Simons gauge
field on the torus. It is shown that there exists a singular gauge
transformation which brings the Hamiltonian to free form. The gauge
transformation removes a degree of freedom from the Hamiltonian. This degree of
freedom generates only a finite dimensional Hilbert space and is responsible
for the component structure of free anyon wave functions. This gives an
understanding of the need for multiple component anyon wave functions from the
point of view of Chern-Simons theory.
