  Pure (2+1)-dimensional Einstein gravity is analysed in the Ashtekar
formulation, when the spatial manifold is a torus. We have found a set of
globally defined observables, forming a closed algebra. This allowed us to
solve the quantum constraints, and to show that the reduced phase space of the
Ashtekar formulation is greater then the corresponding space of the Witten
formulation. Furthermore, we have found a globally defined time variable which
satisfies all the requiriments of an extrinsic time variable in quantum
gravity.
