EQUIVALENT QUANTIZATIONS OF (2+1)-DIMENSIONAL GRAVITY

For spacetimes with the topology R x T2, the action of (2 + 1)-dimensional gravity with negative cosmological constant LAMBDA is written uniquely 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 Hamiltonian. The quantisation of the two classically equivalent formulations differs by terms of order O(HBAR3), negligible for small \LAMBDA\.