EQUIVALENT QUANTIZATIONS OF (2-DIMENSIONAL GRAVITY(1))

For spacetimes with the topology R x T2, the action of (2 + 1)-dimensi onal gravity with negative cosmological constant LAMBDA is written uni quely in terms of the time-independent traces of holonomies around two intersecting noncontractible paths on T2. The holonomy parameters are related to the moduli on slices of constant mean curvature by a time- dependent canonical transformation which introduces an effective Hamil tonian. The quantisation of the two classically equivalent formulation s differs by terms of order O(HBAR3), negligible for small \LAMBDA\.