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