  We write out some sequences of linear maps of vector spaces with fixed bases.
Each term of a sequence is a linear space of differentials of metric values
ascribed to the elements of a simplicial complex - a triangulation of a
manifold. If the sequence turns out to be an acyclic complex then one can
construct a manifold invariant out of its torsion. We demonstrate this first
for three-dimensional manifolds, and then we conduct the part, related to moves
2 <-> 4, of the corresponding work for four-dimensional manifolds.
