  The constraints of $BF$ topological gauge theories are used to construct
Hamiltonians which are anti-commutators of the BRST and anti-BRST operators.
Such Hamiltonians are a signature of Topological Quantum Field Theories
(TQFT's). By construction, both classes of topological field theories share the
same phase spaces and constraints. We find that, for 2+1 and 1+1 dimensional
space-times foliated as $M=\Sigma\times\IR$, a homomorphism exists between the
constraint algebras of our TQFT and those of canonical gravity. The metrics on
the two-dimensional hypersurfaces are also obtained.
