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Regular and Chaotic Dynamics, 2018, Volume 23, Issue 1, Pages 47–53
DOI: https://doi.org/10.1134/S1560354718010045 (Mi rcd307) 		 
Zeroth Poisson Homology, Foliated Cohomology and Perfect Poisson Manifolds

David Martínez-Torresa, Eva Mirandabc

a Department of Mathematics, Pontificia Universidade do Rio de Janeiro, Rua Marquês de São Vicente, 225, Gávea - Rio de Janeiro, CEP 22451-900, Brazil
b Department of Mathematics-UPC and BGSMath, Barcelona, Spain
c CEREMADE (Université de Paris Dauphine), IMCCE (Observatoire de Paris), and IMJ (Université de Paris Diderot), 77 Avenue Denfert Rochereau, Paris, 75014, France
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DOI: https://doi.org/10.1134/S1560354718010045
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.
Keywords: Poisson homology, foliated cohomology.
Funding agency Grant number
Ministerio de Economía y Competitividad MTM2015-69135-P/FEDER
Generalitat de Catalunya 2014SGR634
Agence Nationale de la Recherche ANR-10-LABX- 0098
Eva Miranda is supported by the Catalan Institution for Research and Advanced Studies via an ICREA Academia 2016 Prize, by a Chaire d’Excellence de la Fondation Sciences Mathématiques de Paris, and partially supported by the Ministerio de Economía y Competitividad project with reference MTM2015-69135-P/FEDER and by the Generalitat de Catalunya project with reference 2014SGR634. This work is supported by a public grant overseen by the French National Research Agency (ANR) as part of the “Investissements d’Avenir” program (reference: ANR-10-LABX-0098). Part of this research has been supported by an Ajut mobilitat 2017-EPSEB.
Received: 05.09.2017
Accepted: 20.11.2017
Bibliographic databases:
Document Type: Article
MSC: 53D17, 53C12
Language: English
Citation: David Martínez-Torres, Eva Miranda, “Zeroth Poisson Homology, Foliated Cohomology and Perfect Poisson Manifolds”, Regul. Chaotic Dyn., 23:1 (2018), 47–53
Citation in format AMSBIB
\Bibitem{MarMir18}
\by David Mart{\'\i}nez-Torres, Eva Miranda
\paper Zeroth Poisson Homology, Foliated Cohomology and Perfect Poisson Manifolds
\jour Regul. Chaotic Dyn.
\yr 2018
\vol 23
\issue 1
\pages 47--53
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