  By making use of the complete decomposition of SO(3) spin connection, the
topological defect in 3-dimensional Euclidean gravity is studied in detail. The
topological structure of disclination is given as the combination of a monopole
structure and a vortex structure. Furthermore, the Kac-Moody algebra generated
by the monopole and vortex is discussed in three dimensional Chern-Simons
theory.
