## Osaka Journal of Mathematics

### Formality and hard Lefschetz property of aspherical manifolds

Hisashi Kasuya

#### 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.

#### Article information

Source
Osaka J. Math., Volume 50, Number 2 (2013), 439-455.

Dates
First available in Project Euclid: 21 June 2013

https://projecteuclid.org/euclid.ojm/1371833494

Mathematical Reviews number (MathSciNet)
MR3080809

Zentralblatt MATH identifier
1283.53068

#### Citation

Kasuya, Hisashi. Formality and hard Lefschetz property of aspherical manifolds. Osaka J. Math. 50 (2013), no. 2, 439--455. https://projecteuclid.org/euclid.ojm/1371833494

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