Cohomologies of locally conformally symplectic manifolds and solvmanifolds
type: Item
instance of: scholarly article
title: Cohomologies of locally conformally symplectic manifolds and solvmanifolds
zbMATH Open document ID: 1394.32022
author: Daniele Angella
author: Alexandra Otiman
author: Nicoletta Tardini
published in: Annals of Global Analysis and Geometry
publication date: 2018-01-25T00:00:00Z
full work available at URL: https://arxiv.org/abs/1703.05512
review text: Let \(X\) be a compact differentiable manifold and let \(\Omega\) be a locally conformal symplectic (lcs) form on \(X\), let \(\theta\) be the Lee form and let \(d_{\theta}:=d- (\theta \wedge-)\) be the twisted differential. Lcs cohomologies on \(X\) are introduced and studied. Precisely, a bi-differential graded vector space structure is introduced and its associated cohomologies are investigated: Morse-Novikov cohomology and its lcs-dual, lcs Bott-Chern and Aeppli cohomologies. The elliptic Hodge theory, the Poincaré duality, and the hard Lefschetz condition are studied. Moreover explicit examples are described on nilmanifolds, solvmanifolds and Oeljeklaus-Toma manifolds. It is proved that Inoue surfaces of type \(S^0\) and in general Oeljeklaus-Toma manifolds with one complex plane satisfy the Mostow property.
reviewed by: Antonella Nannicini
Mathematics Subject Classification ID: 32Q99
Mathematics Subject Classification ID: 53A30
Mathematics Subject Classification ID: 32C35
zbMATH DE Number: 6829771
zbMATH Keywords: locally conformally symplectic form
zbMATH Keywords: cohomology
zbMATH Keywords: non-Kähler geometry
describes a project that uses: SageMath
MaRDI profile type: Publication
OpenAlex ID: W3098842703
arXiv ID: 1703.05512
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DOI: 10.1007/S10455-017-9568-Y
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