  It is known that if gauge conditions have Gribov zero modes, then topological
symmetry is broken. In this paper we apply it to topological gravity in
dimension $n \geq 3$. Our choice of the gauge condition for conformal
invariance is $R+{\alpha}=0$ , where $R$ is the Ricci scalar curvature. We find
when $\alpha \neq 0$, topological symmetry is not broken, but when $\alpha =0$
and solutions of the Einstein equations exist then topological symmetry is
broken. This conditions connect to the Yamabe conjecture. Namely negative
constant scalar curvature exist on manifolds of any topology, but existence of
nonnegative constant scalar curvature is restricted by topology. This fact is
easily seen in this theory. Topological symmetry breaking means that BRS
symmetry breaking in cohomological field theory. But it is found that another
BRS symmetry can be defined and physical states are redefined. The divergence
due to the Gribov zero modes is regularized, and the theory after topological
symmetry breaking become semiclassical Einstein gravitational theory under a
special definition of observables.
