  The perturbative finiteness of various topological models (e.g. BF models)
has its origin in an extra symmetry of the gauge-fixed action, the so-called
vector supersymmetry. 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 first extend vector supersymmetry of BF
models to generic manifolds by incorporating it into the BRST symmetry within
the Batalin-Vilkovisky framework. Thereafter, we address the relationship
between gravity and BF models, in particular for three-dimensional space-time.
