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The canonical analysis and subsequent quantization of the (2+1)-dimensionalaction of pure gravity plus a cosmological constant term is considered, underthe assumption of the existence of one spacelike Killing vector field. Theproper imposition of the quantum analogues of the two linear (momentum)constraints reduces an initial collection of state vectors, consisting of allsmooth functionals of the components (and/or their derivatives) of the spatialmetric, to particular scalar smooth functionals. The demand that themidi-superspace metric (inferred from the kinetic part of the quadratic(Hamiltonian) constraint) must define on the space of these states an inducedmetric whose components are given in terms of the same states, which is madepossible through an appropriate re-normalization assumption, severely reducesthe possible state vectors to three unique (up to general coordinatetransformations) smooth scalar functionals. The quantum analogue of theHamiltonian constraint produces a Wheeler-DeWitt equation based on this reducedmanifold of states, which is completely integrated.

Towards Canonical Quantum Gravity for G1 Geometries in 2+1 Dimensions with a Lambda--Term