Equivalent quantisations of (2+1)-dimensional gravity

For spacetimes with the topology Image , the action of (2+1)-dimensional gravity with negative cosmological constant Λ 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(ħ3), negligible for small |Λ|.