  Using a smooth triangulation and a Riemannian metric on a compact, connected,
closed manifold M of dimension n we have got that every such M can be
represented as a union of a n-dimensional cell and a connected union K of some
subsimplexes of the triangulation. A sufficiently small closed neighborhood of
K is called a geometric black hole. Any smooth tensor field T (or other
structure) can be deformed into a continuous and sectionally smooth tensor
field T1 where T1 has a very simple construction out of the black hole.
