2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/192195It 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 $\frac {2π}{k}$ and $k$ is an integer entering the Chern-Simons action.12 pages, latex, no figuresHigh Energy Physics - Theorytext