  We apply the Godbillon-Vey class to compute the transition amplitudes between
some non-commutative solitons in M-Theory; our context is that of
Connes-Douglas-Schwarz where they considered compactifications of matrix models
on noncommutative tori. Two important consequences follow: we describe a new
normalisation for the Abelian Chern-Simons theory using symplectic 4-manifolds
as providing cobordisms for tight contact 3-manifolds and we construct a new(?)
invariant for 3-manifolds. Moreover we modify the topological Lagrangian
density suggested for M-Theory in a previous article to a \textsl{quadratic}
one using the fact that the \emph{functor of immersions is a linearisation (or
``the differential'') of the functor of embeddings}
