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SU(2) flat connection on 2D Riemann surface is shown to relate to thegeneralized twisted geometry in 3D space with cosmological constant. Variousflat connection quantities on Riemann surface are mapped to the geometricalquantities in discrete 3D space. We propose that the moduli space of SU(2) flatconnections on Riemann surface generalizes the phase space of twisted geometryor Loop Quantum Gravity to include the cosmological constant.

SU(2) Flat Connection on Riemann Surface and Twisted Geometry with Cosmological Constant