Formality and hard Lefschetz property of aspherical manifolds

Hisashi Kasuya

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 $K(\Gamma ,1)$…