Some lagrangian invariants of symplectic manifolds
Volume 76 / 2007
Banach Center Publications 76 (2007), 515-525
MSC: Primary 55N35, 53B05, 55T10; Secondary 17B40, 17B55.
DOI: 10.4064/bc76-0-27
Abstract
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 ${\cal A}_{F}$ (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 $H^{q}({\cal A}_{F},V^{F})\times H_{q}({\cal A}_{F},V^{F})\rightarrow V^{F}$, which is invariant under $F$-preserving symplectic diffeomorphisms.
