A six dimensional compact symplectic solvmanifold without Kähler structures
type: Item
instance of: scholarly article
title: A six dimensional compact symplectic solvmanifold without Kähler structures
zbMATH Open document ID: 0861.53032
author: Manuel de León
author: Marisa Fernández
author: Martintxo Saralegi-Aranguren
published in: Osaka Journal of Mathematics
publication date: 1997-05-13T00:00:00Z
review text: The authors conjecture that a compact solvmanifold has a Kähler structure if and only if it is a finite quotient of a complex torus. The purpose of the paper is to construct a compact symplectic (non-nilpotent) solvmanifold \(M^6=\Gamma/G\) of dimension six for which either the Hard Lefschetz Theorem does not hold or the minimal model of \(M\) is not formal. Hence \(M\) does not admit a Kähler structure. They show that the minimal model of \(M^6\) is not formal by proving that there are nontrivial (quadruple) Massey products and remark that all (triple) Massey products of \(M^6\) vanish. For \(G\) a real Lie group of dimension \(2n\) they show that the space of left invariant almost complex structures on \(G\) has dimension \(2n^2\) and \(G\) has no left invariant complex structures.
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 902852
zbMATH Keywords: symplectic manifold
zbMATH Keywords: solvmanifold
zbMATH Keywords: Kähler structure
reviewed by: Stanisław Janeczko
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 902852