  We propose the theory of quantum gravity with interactions introduced by
topological principle. The fundamental property of such a theory is that its
energy-momentum tensor is an BRST anticommutator. Physical states are elements
of BRST cohomology group. The model with only topological excitations,
introduced recently by Witten is discussed from the point of view of induced
gravity program. We find that the mass scale is induced dynamically by
gravitational instantons. The low energy effective theory has gravitons, which
occur as the collective excitations of geometry, when the metric becomes
dynamical. Applications of cobordism theory to QG are discussed.
