This talk explains the relation between a class of flat connections on a 3-manifold and the constant curvature simplicial geometries in 4-dimensions. The quantization of 4d simplicial geometry can be carried out via the quantization of flat connection on 3-manifold. Such a procedure gives a relation between quantum SL(2,C) Chern-Simons theory on 3-manifold and Loop Quantum Gravity on 4-manifold.