  We propose a reduced constrained Hamiltonian formalism for the exactly
soluble $B \wedge F$ theory of flat connections and closed two-forms over
manifolds with topology $\Sigma^3 \times (0,1)$. The reduced phase space
variables are the holonomies of a flat connection for loops which form a basis
of the first homotopy group $\pi_1(\Sigma^3)$, and elements of the second
cohomology group of $\Sigma^3$ with value in the Lie algebra $L(G)$. When
$G=SO(3,1)$, and if the two-form can be expressed as $B= e\wedge e$, for some
vierbein field $e$, then the variables represent a flat spacetime. This is not
always possible: We show that the solutions of the theory generally represent
spacetimes with ``global torsion''. We describe the dynamical evolution of
spacetimes with and without global torsion, and classify the flat spacetimes
which admit a locally homogeneous foliation, following Thurston's
classification of geometric structures.
