THE FLAT OSP(1,2 2) SUPERCONNECTION CONDITION - 2-D SUPERGRAVITY AND TOPOLOGICAL 2-D GRAVITY/

We consider pure 2 - d supergravity as a flat OSp(1, 2/2) superconnect ion of a super-gauge field theory on a (2,2) - d supermanifold. From a n appropriate Wigner-Inonu contraction of the OSp(1,2/2) algebra, we s how that the superzweibein E(M)A and the U(1) superconnection OMEGA(M) of 2 - d supergravity transmute into BRST multiplets composed of the fields, their ghosts and the auxiliary fields of gauge theory of topol ogical 2 - d gravity. These fields and their topological BRST transfor mations can be recast in this geometric formalism where the ''gravitin o'' now plays the role of ghost related to the zweibein shift of topol ogical 2 - d gravity. We close this paper by constructing a gauge fixe d term of the quantum action in terms of superfield.