  Topological gravity is the reduction of Einstein's theory to spacetimes with
vanishing curvature, but with global degrees of freedom related to the topology
of the universe. We present an exact Hamiltonian lattice theory for topological
gravity, which admits translations of the lattice sites as a gauge symmetry.
There are additional symmetries, not present in Einstein's theory, which kill
the local degrees of freedom. We show that these symmetries can be fixed by
choosing a gauge where the torsion is equal to zero. In this gauge, the theory
describes flat space-times. We propose two methods to advance towards the holy
grail of lattice gravity: A Hamiltonian lattice theory for curved space-times,
with first-class translation constraints.
