Cohomological aspects on complex and symplectic manifolds
type: Item
instance of: scholarly article
title: Cohomological aspects on complex and symplectic manifolds
zbMATH Open document ID: 1402.53061
DOI: 10.1007/978-3-319-62914-8_17
author: Nicoletta Tardini
publication date: 2018-05-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/1612.04764
review text: This is a survey paper that describes how Bott-Chern and Aeppli cohomology groups are important in the study of non-Kähler geometry. Namely, the topological invariants of the de Rham cohomology groups and the complex invariants of the Dolbeault cohomology groups are non-significant in the non-Kähler setting. The paper mainly describes previous results of the author and co-workers expecially related to the study of the \(\partial{\bar{\partial}}\)-lemma. Moreover, symplectic versions of the Bott-Chern and Aeppli cohomologies, introduced by \textit{L.-S. Tseng} and \textit{S.-T. Yau} [J. Differ. Geom. 91, No. 3, 383--416 (2012; Zbl 1275.53079)], are described and a characterization of the Hard Lefschetz Condition is given. For the entire collection see [Zbl 1387.53005].
reviewed by: Antonella Nannicini
Mathematics Subject Classification ID: 53D05
Mathematics Subject Classification ID: 32Q60
zbMATH DE Number: 6866495
zbMATH Keywords: complex manifolds
zbMATH Keywords: symplectic manifolds
zbMATH Keywords: cohomology groups
zbMATH Keywords: \(\partial \bar{\partial}\)-lemma
MaRDI profile type: Publication
OpenAlex ID: W2589737327
arXiv ID: 1612.04764
description: scientific article