Remarks on the Lichnerowicz-Poisson cohomology
type: Item
instance of: scholarly article
title: Remarks on the Lichnerowicz-Poisson cohomology
zbMATH Open document ID: 0708.58010
author: Izu Vaisman
publication date: 1990-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/74907
review text: The paper begins with some general remarks which include the Mayer- Vietoris exact sequence, a covariant version of the Lichnerowicz-Poisson cohomology, and the definition of an associated Serre-Hochschild spectral sequence. Then we consider the regular case, and we discuss the Poisson cohomology by using a natural bigrading of the Lichnerowicz cochain complex. Furthermore, if the symplectic foliation of the Poisson manifold is either transversally Riemannian or transversally symplectic, the spectral sequence mentioned above is determined by the leafwise cohomologies of the foliation, and if, moreover, the Poisson structure is transversally constant, the spectral sequence defines the Lichnerowicz- Poisson cohomology in a straightforward manner.
reviewed by: Izu Vaisman
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 58A12
zbMATH DE Number: 4163766
zbMATH Keywords: Lichnerowicz-Poisson cohomology
zbMATH Keywords: Serre-Hochschild spectral sequence
zbMATH Keywords: Poisson manifold
MaRDI profile type: Publication
OpenAlex ID: W2321816247
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DOI: 10.5802/AIF.1243
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 4163766