Geodesic
Physical phase space of the lattice Yang–Mills theory and moduli space of flat connections on a Riemann surface
Teoretičeskaâ i matematičeskaâ fizika, Tome 113 (1997) no. 1, pp. 100-111 
S. A. Frolov. Physical phase space of the lattice Yang–Mills theory and moduli space of flat connections on a Riemann surface. Teoretičeskaâ i matematičeskaâ fizika, Tome 113 (1997) no. 1, pp. 100-111. http://geodesic.mathdoc.fr/item/TMF_1997_113_1_a8/
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It is shown that the physical phase space of $\gamma$-deformed, Hamiltonian-lattice Yang–Mills theory, which was recently proposed in [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, respectively, the total number of links and vertices of the lattice. The deformation parameter $\gamma$ is identified with $2\pi/k$ and $k$ is an integer entering the Chern–Simons action.

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