An interacting geometry model and induced gravity

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 a BRST anticommutator. Physical states are elements of the BRST cohomology group. The model with only topological excitations, introduced recently by Witten, is discussed from the point of view of the 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 quantum gravity are discussed.This essay received the second award from the Gravity Research Foundation for the year 1988.—Ed.