Dolbeault-Massey triple products of low degree
type: Item
instance of: scholarly article
title: Dolbeault-Massey triple products of low degree
zbMATH Open document ID: 1329.32013
author: Andrea Cattaneo
author: Adriano Tomassini
published in: Journal of Geometry and Physics
publication date: 2015-11-13T00:00:00Z
review text: The authors characterize the non-vanishing of special Dolbeault-Massey triple products of low degree in differential bigraded algebras, with applications to the Dolbeault complex of compact complex manifolds. Dolbeault-Massey products are obstructions to Dolbeault formality in the sense of [\textit{J. Neisendorfer} and \textit{L. Taylor}, Trans. Am. Math. Soc. 245, 183--210 (1978; Zbl 0441.55014)]. In particular, the Dolbeault complex of compact complex manifolds satisfying the \(\partial\overline\partial\)-Lemma is Dolbeault formal. The main result is Theorem 3.2, which characterizes when the Dolbeault-Massey triple product \(\left\langle [X], [X], [Y] \right\rangle\) is non-vanishing, where \(X\) is of bidegree \((1,0)\) and \(Y\) is of bidegree \((0,1)\).
reviewed by: Daniele Angella
Mathematics Subject Classification ID: 32Q99
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 32C35
zbMATH DE Number: 6508432
zbMATH Keywords: differential bigraded algebra
zbMATH Keywords: formality
zbMATH Keywords: Massey triple product
zbMATH Keywords: Dolbeault-Massey triple product
MaRDI profile type: Publication
full work available at URL: j.geomphys.2015.08.016
OpenAlex ID: W2289689786
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DOI: 10.1016/J.GEOMPHYS.2015.08.016
description: scientific article; zbMATH DE number 6508432