Abstract
For a Lie group $G = \mathbb{R}^{n}\ltimes_{\phi}\mathbb{R}^{m}$ with the semi-simple action $\phi\colon \mathbb{R}^{n}\to \Aut(\mathbb{R}^{m})$, 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.
Citation
Hisashi Kasuya. "Formality and hard Lefschetz property of aspherical manifolds." Osaka J. Math. 50 (2) 439 - 455, June 2013.
Information