Osaka Journal of Mathematics
- Osaka J. Math.
- Volume 50, Number 2 (2013), 439-455.
Formality and hard Lefschetz property of aspherical manifolds
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
Permanent link to this document
https://projecteuclid.org/euclid.ojm/1371833494
Mathematical Reviews number (MathSciNet)
MR3080809
Zentralblatt MATH identifier
1283.53068
Subjects
Primary: 20F16: Solvable groups, supersolvable groups [See also 20D10] 55P20: Eilenberg-Mac Lane spaces 55P62: Rational homotopy theory
Secondary: 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx] 32J27: Compact Kähler manifolds: generalizations, classification
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
