Formality and hard Lefschetz property of aspherical manifolds

Abstract

For a Lie group $G={\mathbb{R}}^n{⋉}_{\varphi }{\mathbb{R}}^m$ with the semi-simple action $\varphi :{\mathbb{R}}^n\to \mathrm{Aut}({\mathbb{R}}^m)$, we show that if $\Gamma$ is a finite extension of a lattice of $G$ then $K(\Gamma ,1)$ is formal. Moreover we show that a compact symplectic aspherical manifold with the fundamental group $\Gamma$ satisfies the hard Lefschetz property. By those results we give many examples of formal solvmanifolds satisfying the hard Lefschetz property but not admitting Kähler structures.

14 pages to appear in Osaka J. Math

References in corpus (2)

• On Low-Dimensional Solvmanifolds
• Kähler Solvmanifolds

Cited by in corpus (4)

• Vaisman metrics on solvmanifolds and Oeljeklaus-Toma manifolds
• Hodge symmetry and decomposition on non-Kähler solvmanifolds
• Minimal models, formality and hard Lefschetz properties of solvmanifolds with local systems
• Coeffective cohomology of symplectic aspherical manifolds