  Geometric quantization of 2+1 dimensional pure Yang-Mills theory is studied
with focusing on finite large scales. It is previously shown that (Yildirim,
2015, Int. J. Mod. Phys A, 30(7), 1550034), topologically massive Yang-Mills
theory exhibits a Chern-Simons splitting behavior at large scales, similar to
the topologically massive AdS gravity model in its near Chern-Simons limit.
This splitting occurs as two Chern-Simons parts with levels $+k/2$ each, where
$k$ is the original Chern-Simons level in the Lagrangian. In the pure
Chern-Simons limit, split parts combine to give the original Chern-Simons
level. The opposite limit of the gravitational analogue gives an
Einstein-Hilbert term with a negative cosmological constant, which can be
written as a two half Chern-Simons terms with opposite signs. With this
motivation, the gauge theory analogue of this limit is investigated, showing
that at finite large distances pure Yang-Mills theory acts like a topological
theory that consists of split Chern-Simons parts with levels $+k/2$ and $-k/2$.
At very large distances these split terms cancel, making the Yang-Mills theory
trivial, as expected, due to the existence of a mass gap. Gauge invariance of
the split parts is discussed. It is also shown that this splitting behavior can
be exploited to incorporate link invariants of knot theory, just like in the
topologically massive case.
