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Some lagrangian invariants of symplectic manifolds

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Boyom M.

Banach Center Publications

2007

tom 76

nr 1

515-525

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 $H^{q}(𝓐_{F},V^{F}) × H_{q}(𝓐_{F},V^{F}) → V^{F}$, which is invariant under F-preserving symplectic diffeomorphisms.

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1 Banach Center Publications

1 Boyom M.

1 2007

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Some lagrangian invariants of symplectic manifolds