On the flux homomorphism for regular Poisson manifolds

Rybicki, Tomasz

Displaying similar documents to “On the flux homomorphism for regular Poisson manifolds”

Complementary 2-forms of Poisson structures

Izu Vaisman (1996)

Compositio Mathematica

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Almost product structures and Poisson reduction of presymplectic systems.

Manuel de León, David Martín de Diego (1995)

Extracta Mathematicae

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Gauge equivalence of Dirac structures and symplectic groupoids

Henrique Bursztyn, Olga Radko (2003)

Annales de l’institut Fourier

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We study gauge transformations of Dirac structures and the relationship between gauge and Morita equivalences of Poisson manifolds. We describe how the symplectic structure of a symplectic groupoid is affected by a gauge transformation of the Poisson structure on its identity section, and prove that gauge-equivalent integrable Poisson structures are Morita equivalent. As an example, we study certain generic sets of Poisson structures on Riemann surfaces: we find complete gauge-equivalence...

Remarks on the Lichnerowicz-Poisson cohomology

Izu Vaisman (1990)

Annales de l'institut Fourier

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The paper begins with some general remarks which include the Mayer-Vietoris exact sequence, a covariant version of the Lichnerowicz-Poisson cohomology, and the definition of an associated Serre-Hochshild spectral sequence. Then we consider the regular case, and we discuss the Poisson cohomology by using a natural bigrading of the Lichnerowicz cochain complex. Furthermore, if the symplectic foliation of the Poisson manifold is either transversally Riemannian or transversally symplectic,...

On submanifolds and quotients of Poisson and Jacobi manifolds

Charles-Michel Marle (2000)

Banach Center Publications

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We obtain conditions under which a submanifold of a Poisson manifold has an induced Poisson structure, which encompass both the Poisson submanifolds of A. Weinstein [21] and the Poisson structures on the phase space of a mechanical system with kinematic constraints of Van der Schaft and Maschke [20]. Generalizations of these results for submanifolds of a Jacobi manifold are briefly sketched.