Some lagrangian invariants of symplectic manifolds

Michel Nguiffo Boyom

Banach Center Publications, Tome 75 (2007), p. 515-525 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $_{F}$ (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 $H^{q} (_{F}, V^{F}) \times H_{q} (_{F}, V^{F}) \to V^{F}$ , which is invariant under F-preserving symplectic diffeomorphisms.

Publié le : 2007-01-01

Zbl 1123.55002

EUDML-ID : urn:eudml:doc:281826

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     author = {Michel Nguiffo Boyom},
     title = {Some lagrangian invariants of symplectic manifolds},
     journal = {Banach Center Publications},
     volume = {75},
     year = {2007},
     pages = {515-525},
     zbl = {1123.55002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc76-0-27}
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Michel Nguiffo Boyom. Some lagrangian invariants of symplectic manifolds. Banach Center Publications, Tome 75 (2007) pp. 515-525. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc76-0-27/