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Zeroth Poisson Homology, Foliated Cohomology and Perfect Poisson Manifolds

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Abstract

We prove that, for compact regular Poisson manifolds, the zeroth homology group is isomorphic to the top foliated cohomology group, and we give some applications. In particular, we show that, for regular unimodular Poisson manifolds, top Poisson and foliated cohomology groups are isomorphic. Inspired by the symplectic setting, we define what a perfect Poisson manifold is. We use these Poisson homology computations to provide families of perfect Poisson manifolds.

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Authors and Affiliations

  1. Department of Mathematics, Pontificia Universidade do Rio de Janeiro Rua Marquês de São Vicente, 225, Gávea - Rio de Janeiro, CEP, São Vicente, 22451-900, Brazil

    David Martínez-Torres

  2. Department of Mathematics-UPC and BGSMath, Barcelona, Spain

    Eva Miranda

  3. CEREMADE (Université de Paris Dauphine), IMCCE (Observatoire de Paris), and IMJ (Université de Paris Diderot), 77 Avenue Denfert Rochereau, Paris, 75014, France

    Eva Miranda

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  1. David Martínez-Torres
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  2. Eva Miranda
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Correspondence to David Martínez-Torres.

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Martínez-Torres, D., Miranda, E. Zeroth Poisson Homology, Foliated Cohomology and Perfect Poisson Manifolds. Regul. Chaot. Dyn. 23, 47–53 (2018). https://doi.org/10.1134/S1560354718010045

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  • DOI: https://doi.org/10.1134/S1560354718010045

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