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A theory of topological gravity with an independent vierbein and spin connection is formulated in four space-time dimensions. Topological symmetries, as well as local Lorentz transformations and diffeomorphisms, are fixed, following the formalism of Batalin and Vilkovisky. The gauge-fixing conditions of the topological symmetries are chosen in such a way that self-duality is preserved for both curvature and torsion two-forms. It is shown that these gauge-fixing conditions have nontrivial classical solutions. Nontrivial observables are also constructed.
Nakamichi et al. (Sun,) studied this question.