  For spacetimes with the topology $\IR\!\times\!T^2$, the action of
(2+1)-dimensional gravity with negative cosmological constant $\La$ is written
uniquely in terms of the time-independent traces of holonomies around two
intersecting noncontractible paths on $T^2$. The holonomy parameters are
related to the moduli on slices of constant mean curvature by a time-dependent
canonical transformation which introduces an effective Hamiltonian. The
quantisation of the two classically equivalent formulations differs by terms of
order $O(\hbar^3)$, negligible for small $|\La|$.
