  We show that Chern-Simons gauge theory with appropriate cutoffs is
equivalent, term by term in perturbation theory, to a Fermionic theory with a
nonlocal interaction term. When an additional cutoff is placed on the Fermi
fields, this Fermionic theory gives rise to a convergent perturbation
expansion. This leads us to conjecture that Chern-Simons gauge theory also
gives rise to convergent perturbation expansions, which would give a
mathematically well-defined construction of the theory.
