Zeroth poisson homology, foliated cohomology and perfect poisson manifolds

We prove that for 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 sym...

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Detalles Bibliográficos
Autores: Miranda Galcerán, Eva|||0000-0001-9518-5279, Martinez Torres, David
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/119431
Acceso en línea:https://hdl.handle.net/2117/119431
https://dx.doi.org/10.1134/S1560354718010045
Access Level:acceso abierto
Palabra clave:Manifolds (Mathematics)
Poisson homology
foliated cohomology
Varietats (Matemàtica)
Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria diferencial
Descripción
Sumario:We prove that for 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 is a perfect Poisson manifold. We use these Poisson homology computations to provide families of perfect Poisson manifolds.