  Topologically massive Yang-Mills theory is studied in the framework of
geometric quantization. Since this theory has a mass gap proportional to the
topological mass m, Yang-Mills contribution decays exponentially at very large
distances compared to 1/m, leaving a pure Chern-Simons theory with level number
k. In this paper, the near Chern-Simons limit is studied where the distance is
large enough to give an almost topological theory, with a small contribution
from the Yang-Mills term. It is shown that this almost topological theory
consists of two copies of Chern-Simons with level number k/2, very similar to
the Chern-Simons splitting of topologically massive AdS gravity. Also, gauge
invariance of these half-Chern-Simons theories is discussed. As m approaches to
infinity, the split parts add up to give the original Chern-Simons term with
level k. Reduction of the phase space is discussed in this limit. Finally, a
relation between the observables of topologically massive Yang-Mills theory and
Chern-Simons theory is shown. One of the two split Chern-Simons pieces is shown
to be associated with Wilson loops while the other with 't Hooft loops. This
allows one to use skein relations to calculate topologically massive Yang-Mills
theory observables in the near Chern-Simons limit.
