  In Regge calculus the space-time manifold is approximated by certain abstract
simplicial complex, called a pseudo-manifold, and the metric is approximated by
an assignment of a length to each 1-simplex. In this paper for each
pseudomanifold we construct a smooth manifold which we call a manifold with
defects. This manifold emerges from the purely combinatorial simplicial complex
as a result of gluing geometric realizations of its n-simplices followed by
removing the simplices of dimension n-2. The Regge geometry is encoded in a
boundary data of a BF-theory on this manifold. We construct an action
functional which coincides with the standard BF action for suitably regular
manifolds with defects and fields. On the other hand, the action evaluated at
solutions of the field equations satisfying certain boundary conditions
coincides with an evaluation of the Regge action at Regge geometries defined by
the boundary data. As a result we trade the degrees of freedom of Regge
calculus for discrete degrees of freedom of topological BF theory.
