  A four-fermion model in 2+1 dimensions describing N Dirac fermions
interacting via SU(N) invariant N^2-1 four-fermion interactions is solved in
the leading order of the 1/N expansion. The 1/N expansion corresponds to 't
Hoofts topological 1/N expansion in which planar Feynman diagrams prevail. For
the symmetric phase of this model, it is argued that the planar expansion
corresponds to the ladder approximation. A truncated set of Schwinger-Dyson
equations for the fermion propagator and composite boson propagator
representing the relevant planar diagrams is solved analytically. The critical
four-fermion coupling and various critical exponents are determined as
functions of N. The universality class of this model turns out to be quite
distinct from the Gross-Neveu model in the large N limit.
