An \(h\)-principle for symplectic foliations
type: Item
instance of: scholarly article
zbMATH Open document ID: 1245.53033
author: Rui Loja Fernandes
author: Pedro Frejlich
publication date: 2012-05-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/1010.3447
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 53D17
Mathematics Subject Classification ID: 53D05
zbMATH DE Number: 6030244
zbMATH Keywords: almost symplectic foliation
zbMATH Keywords: regularly homotopic
zbMATH Keywords: Poisson bivector
MaRDI profile type: Publication
OpenAlex ID: W2963527393
arXiv ID: 1010.3447
DOI: 10.1093/IMRN/RNR077
published in: IMRN. International Mathematics Research Notices
title: An \(h\)-principle for symplectic foliations
review text: In this paper, the authors prove an \(h\)-principle for symplectic foliations, namely, a \(q\)-codimensional almost symplectic foliation on an open manifold is regularly homotopic to a symplectic foliation. Concerning the problem of deforming a \(q\)-codimensional almost symplectic distribution to an integrable one they show that an almost symplectic distribution on an open manifold with a nondegenerate \(2\)-form is homotopic to a symplectic foliation if and only if the distribution is homotopic to a foliation.NEWLINENEWLINEThis result can be formulated in terms of Poisson geometry saying that a regular bivector \(\pi_0\) on an open manifold is regularly homotopic to a Poisson bivector if and only if the distribution \(Im \pi_0^{\sharp}\) is homotopic to an integrable one.NEWLINENEWLINEIn the end, starting with an example of Bott and modifying it they construct a regular bivector on an open manifold which is not regularly homotopic to a Poisson structure.
reviewed by: Adara M. Blaga
description: scientific article; zbMATH DE number 6030244