  Given a finite connected graph $\Lambda$, the space of $SU(2)$ lattice
gauge-fields on $\Lambda$, modulo gauge transformations, is a Lagrangian
submanifold -- with mild singularities -- of the $SU(2)$ character variety (=
phase-space of Chern-Simons theory) of an associated surface. We present
evidence that, in the limit of large $\Lambda$, integration over the character
variety with respect to the Liouville measure approximates lattice-theoretic
integrals. By the works of W. Goldman, L. Jeffrey and J. Weitsman, the
formalism of Duistermaat-Heckman applies to the relevant integrals over the
character variety. A continuous version of the Verlinde algebra facilitates
computations. In two dimensions we recover standard expressions. For the theory
on a 3-dimensional periodic lattice $\Lambda$ with Migdal action we get a very
pleasant expression for the symplectic partition function, and with the Wilson
action a more elaborate one. Each is a sum of a series with positive terms. One
can also write down expressions for plaquette-plaquette correlations and 't
Hooft loops.
