  SU(2) flat connection on 2D Riemann surface is shown to relate to the
generalized twisted geometry in 3D space with cosmological constant. Various
flat connection quantities on Riemann surface are mapped to the geometrical
quantities in discrete 3D space. We propose that the moduli space of SU(2) flat
connections on Riemann surface generalizes the phase space of twisted geometry
or Loop Quantum Gravity to include the cosmological constant.
