  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.
