On the symmetries of BF models and their relation with gravity

The perturbative niteness of various topological models (e.g. BF models) has its origin in an extra symmetry of the gauge-xed action, the so-called vector su- persymmetry. Since an invariance of this type also exists for gravity and since gravity is closely related to certain BF models, vector supersymmetry should also be useful for tackling various aspects of quantum gravity. With this motivation and goal in mind, we rst extend vector supersymmetry of BF models to generic manifolds by incorporating it into the BRST symmetry within the Batalin-Vilkovisky framework. Thereafter, we ad- dress the relationship between gravity and BF models, in particular for three-dimensional space-time.