Abstract: 
\def\A{{\cal A}}The KV-homology theory is a new framework which yields
interesting properties of lagrangian foliations. This short note
is devoted to relationships between the KV-homology and the
KV-cohomology of a lagrangian foliation. Let us denote by $\A_{F}$
(resp. $V^{F}$) the KV-algebra (resp. the space of basic functions)
of a lagrangian foliation $F$. We show that there exists a pairing
of cohomology and homology to $V^{F}$. That is to say, there is a
bilinear map
$H^{q}(\A_{F},V^{F})\times H_{q}(\A_{F},V^{F})\rightarrow
V^{F}$, which is invariant under $F$-preserving symplectic
diffeomorphisms.

1. UMR CNRS 5149,
   Département de Mathématiques
   Université Montpellier II
   Montpellier, France