  Foliated manifolds are particular examples of noncommutative spaces. In this
article we try to give a qualitative description of the Godbillon-Vey class and
its relation on the one hand to the holonomy and on the other hand to the
topological entropy of a foliation, using a remarkable theorem proved recently
by G. Duminy relating these three notions in the case of codim-1 foliations.
Moreover we shall investigate its possible relation with the black hole entropy
adopting the superstring theory origin of the black hole entropy in the
extremal case. This situation we believe has some striking similarities with
the explanation due to Bellissard of the integrality of the Hall conductivity
in the quantum Hall effect. Our starting point is the Connes-Douglas-Schwarz
article on compactifications of matrix models to noncommutative tori.
