REMARKS ON THE REDUCED PHASE-SPACE OF (2-DIMENSIONAL GRAVITY ON A TORUS IN THE ASHTEKAR FORMULATION(1))

We examine the reduced phase space of the Barbero-Varadarajan solution s of the Ashtekar formulation of (2 + 1)-dimensional general relativit y on a torus; We show that it is a finite-dimensional space due to the existence of an infinite-dimensional residual gauge invariance which reduces the infinite-dimensional space of solutions to a finite-dimens ional space of gauge-inequivalent solutions. This is in agreement with general arguments which imply that the number of physical degrees of freedom for (2 + 1)-dimensional Ashtekar gravity on a torus is finite.