Lattices, cohomology and models of six dimensional almost abelian solvmanifolds

2012/06/26 by Sergio Console, Console, Sergio, Maura Macrì +1 · 2 citations
Mathematics · #22E25 #22E40 #53C30 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:22E25 #msc:22E40 #msc:53C30

paper · pdf · doi:10.48550/arxiv.1206.5977

arXiv admin note: text overlap with arXiv:1003.3774 by other authors

arxiv created 2012/06/26 · openalex publication_date 2012/06/26 · arxiv updated 2012/06/27 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

We construct lattices on six dimensional not completely solvable almost abelian Lie groups, for which the Mostow condition does not hold. For the corresponding compact quotients, we compute the de Rham cohomology (which does not agree in general with the Lie algebra one) and a minimal model. We show that some of these solvmanifolds admit not invariant symplectic structures and we study formality and Lefschetz properties.

Citations

• Non-formal co-symplectic manifolds
• Supersymmetry breaking branes on solvmanifolds and de Sitter vacua in string theory

Cited by

• Six dimensional solvmanifolds with holomorphically trivial canonical bundle
• Lorentzian homogeneous Ricci-flat metrics on almost abelian Lie groups

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