  This is the first in a series of papers where we will derive invariants of
three-manifolds and framed knots in them from the geometry of a manifold
pseudotriangulation put in some way in a four-dimensional Euclidean space.
Thus, the elements of the pseudotriangulation acquire Euclidean geometric
values such as volumes of different dimensions and various kinds of angles.
Then we construct an acyclic complex made of differentials of these geometric
values, and its torsion will lead, depending on the specific kind of this
complex, to some manifold or knot invariants. In this paper, we limit ourselves
to constructing a simplest kind of acyclic complex, from which a three-manifold
invariant can be obtained.
