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The constraints of $BF$ topological gauge theories are used to constructHamiltonians 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 thesame phase spaces and constraints. We find that, for 2+1 and 1+1 dimensionalspace-times foliated as $M=\Sigma\times\IR$, a homomorphism exists between theconstraint algebras of our TQFT and those of canonical gravity. The metrics onthe two-dimensional hypersurfaces are also obtained.Comment: 9 pages, Plain TeX, MIT-CTP#217

DIFF(Σ) AND METRICS FROM HAMILTONIAN-TQFT'S IN 2+1 DIMENSIONS