HOMOGENEOUS (2-DIMENSIONAL GRAVITY IN THE ASHTEKAR FORMULATION(1))

The constraint hypersurfaces defining the Witten and Ashtekar formulat ions for 2+1 gravity are very different. In particular the constraint hypersurface in the Ashtekar case is not a manifold but consists of se veral sectors that intersect each other in a complicated way. The issu e of how to define a consistent dynamics in such a situation is then r ather non-trivial. We discuss this point by working out the details in a simplified (finite-dimensional) homogeneous reduction of 2+1 gravit y in the Ashtekar formulation.