Abstract :
A set of algebraic equations for the topological properties of space-time is derived, and used to extend general relativity into the Planck domain. A unique basis set of three-dimensional prime manifolds is constructed which consists of S3, S1 × S2, and T3. The action of a loop algebra on these prime manifolds yields topological invariants which constrain the dynamics of the four-dimensional space-time manifold. An extended formulation of Machʹs principle and Einsteinʹs equivalence of inertial and gravitational mass is proposed which leads to the correct classical limit of the theory.
