The Topological Structure of the Space-Time Disclination

The space-time disclination is studied by making use of the decomposition theory of gauge potential in terms of antisymmetric tensor field and $\phi$-mapping method. It is shown that the self-dual and anti-self-dual parts of the curvature compose the space-time disclinations which are classified in terms of topological invariants--winding number. The projection of space-time disclination density along an antisymmetric tensor field is quantized topologically and characterized by Brouwer degree and Hopf index.