Q921677
type: Item
instance of: scholarly article
title: Groupoïde d'homotopie d'un feuilletage Riemannien et réalisation symplectique de certaines variétés de Poisson. (Homotopy groupoid of a Riemannian foliation and symplectic realization of certain Poisson manifolds)
zbMATH Open document ID: 0709.58014
DOI: 10.5565/PUBLMAT_33389_01
author: Fernando Alcalde Cuesta
published in: Publicacions Matemàtiques
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/41078
review text: The Hamiltonian vector fields on a Poisson manifold generate a foliation in the sense of Sussmann and Stefan. If it is of dimension 2 and Riemannian, then under some further assumptions the Poisson manifold is shown to admit a symplectic realization in the following sense: there is a symplectic Lie groupoid (so that the graph of the multiplication is a Lagrange submanifold) such that the given Poisson manifold is the space of units and the source and target mappings are Poisson morphisms. On the way to this result it is shown that the homotopy groupoid of a Riemannian foliation is locally trivial.
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 22E99
Mathematics Subject Classification ID: 37C85
zbMATH DE Number: 4166101
zbMATH Keywords: Poisson manifold
zbMATH Keywords: symplectic Lie groupoid
zbMATH Keywords: homotopy groupoid
zbMATH Keywords: Riemannian foliation
reviewed by: Peter W. Michor
MaRDI profile type: Publication
OpenAlex ID: W2147630813
label: Groupoïde d'homotopie d'un feuilletage Riemannien et réalisation symplectique de certaines variétés de Poisson. (Homotopy groupoid of a Riemannian foliation and symplectic realization of certain Poisson manifolds)
description: scientific article; zbMATH DE number 4166101