Email this article Zeroth Poisson Homology, Foliated Cohomology and Perfect Poisson Manifolds
- Authors: Martínez-Torres D.1, Miranda E.2,3
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Affiliations:
- Department of Mathematics
- Department of Mathematics-UPC and BGSMath
- CEREMADE (Université de Paris Dauphine), IMCCE (Observatoire de Paris), and IMJ (Université de Paris Diderot)
- Issue: Vol 23, No 1 (2018)
- Pages: 47-53
- Section: Article
- URL: https://journals.rcsi.science/1560-3547/article/view/218907
- DOI: https://doi.org/10.1134/S1560354718010045
- ID: 218907
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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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About the authors
David Martínez-Torres
Department of Mathematics
Author for correspondence.
Email: dfmtorres@gmail.com
Brazil, 225, Gávea - Rio de Janeiro, CEP, São Vicente, 22451-900
Eva Miranda
Department of Mathematics-UPC and BGSMath; CEREMADE (Université de Paris Dauphine), IMCCE (Observatoire de Paris), and IMJ (Université de Paris Diderot)
Email: dfmtorres@gmail.com
Spain, Barcelona; 77 Avenue Denfert Rochereau, Paris, 75014
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