Topological gravity with exchange algebra

A topological gravity is obtained by twisting the effective $(2,0)$ super\-gravity. 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 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.