  It is shown that the physical phase space of $\g$-deformed Hamiltonian
lattice Yang-Mills theory, which was recently proposed in refs.[1,2], coincides
as a Poisson manifold with the moduli space of flat connections on a Riemann
surface with $(L-V+1)$ handles and therefore with the physical phase space of
the corresponding $(2+1)$-dimensional Chern-Simons model, where $L$ and $V$ are
correspondingly a total number of links and vertices of the lattice. The
deformation parameter $\g$ is identified with $\frac {2\pi}{k}$ and $k$ is an
integer entering the Chern-Simons action.
