  A topological extension of general relativity is presented. The superposition
principle of quantum mechanics, as formulated by the Feynman path integral, is
taken as a starting point. It is argued that the trajectories that enter this
path integral are distinct, despite any quantum uncertainty in geometry, and
thus that space-time topology is multiply connected. Specifically, space-time
at the Planck scale consists of a lattice of three-tori that facilitates many
distinct paths for particles to travel along. To add gravity, mini black holes
are attached to this lattice. These mini black holes represent Wheeler's
quantum foam and result from the fact that GR is not conformally invariant. The
stable creation of such mini black holes is found to be caused by the existence
of macroscopic (so long-lived) black holes. This connection, by which
macroscopic black holes induce mini black holes, is a topological expression of
Mach's principle. The proposed topological extension of GR can be tested
because, if correct, the dark energy density of the universe should be linearly
proportional to the total number of macroscopic black holes in the universe at
any time. This prediction, although strange, agrees with current astrophysical
observations.
