Lattices, cohomology and models of six dimensional almost abelian\n solvmanifolds

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

paper · pdf · doi:10.48550/arxiv.1206.5977

openalex publication_date 2012/06/26 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Non-formal co-symplectic manifolds

Cited by

• Six dimensional solvmanifolds with holomorphically trivial canonical bundle

Related

• Formality and symplectic structures of almost abelian solvmanifolds
• Hard Lefschetz Condition on symplectic non-Kähler solvmanifolds
• Cohomological properties of unimodular six dimensional solvable Lie\n algebras
• Hermitian structures on six-dimensional almost nilpotent solvmanifolds
• Almost-complex invariants of families of six-dimensional solvmanifolds