  We show that 2+1-dimensional Euclidean quantum gravity is equivalent, under
some mild topological assumptions, to a Gaussian fermionic system. In
particular, for manifolds topologically equivalent to $\Sigma_g\times\RrR$ with
$\Sigma_g$ a closed and oriented Riemann surface of genus $g$, the
corresponding 2+1-dimensional Euclidean quantum gravity may be related to the
3D-lattice Ising model before its thermodynamic limit.
