  We use the notation EX(S>M), EXF(S>M) and DL(S>M), where M is a smooth
manifold and S is a geometric structure. EX(S>M) is the question whether S
exists in M. EXF(S>M) is the question whether M admits S-foliations. DL(S>M) is
the search of an invariant measuring how M is far from admitting S. For many
major geometric structures, those questions are widly open. In this paper, we
address EX(S>M), EXF(S>M) and DL(S>M) for affine structure and symplectic
structure, left invariant affine structure, left invariant symplectic structure
and bi-invariant riemanniann structure in Lie groups
