TOPOLOGICAL GRAVITY WITH EXCHANGE ALGEBRA

A topological gravity is obtained by twisting the effective (2, 0) supergravity. We show that this topological gravity has an infinite number of BRST invariant quantities with conformal weight 0. They are a tower of OSp(2, 2) multiplets and satisfy the classical exchange algebra of OSp(2, 2). We argue that these BRST invariant quantities become physical operators in the quantum theory and that their correlation functions are braided according to the quantum OSp(2, 2) group. These properties of the topological effective gravity are not shared by the standard topological gravity.