The modular class of a regular Poisson manifold and the Reeb invariant of its symplectic foliation

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dc.creatorAbouqateb, A.
dc.creatorBoucetta, M.
dc.date2002-11-26
dc.date.accessioned2026-07-07T04:53:18Z
dc.date.available2026-07-07T04:53:18Z
dc.descriptionWe show that, for any regular Poisson manifold, there is an injective natural linear map from the first leafwise cohomology space into the first Poisson cohomology space which maps the Reeb class of the symplectic foliation to the modular class of the Poisson manifold. The Riemannian interpretation of those classes will permit us to show that a regular Poisson manifold whose symplectic foliation is of codimension one is unimodular if and only if its symplectic foliation is Riemannian foliation. It permit us also to construct examples of unimodular Poisson manifolds and other which are not unimodular. Finally, we prove that the first leafwise cohomology is an invariant of Morita equivalence.
dc.description11 pages
dc.identifierhttps://arxiv.org/abs/math/0211405
dc.identifierhttp://arxiv.org/abs/math/0211405
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/65792
dc.subjectDifferential Geometry
dc.subjectSymplectic Geometry
dc.subjectPrimary 53D17 ; Secondary 53C12
dc.titleThe modular class of a regular Poisson manifold and the Reeb invariant of its symplectic foliation
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