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June 2013 Formality and hard Lefschetz property of aspherical manifolds
Hisashi Kasuya
Osaka J. Math. 50(2): 439-455 (June 2013).

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

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Hisashi Kasuya. "Formality and hard Lefschetz property of aspherical manifolds." Osaka J. Math. 50 (2) 439 - 455, June 2013.

Information

Published: June 2013
First available in Project Euclid: 21 June 2013

zbMATH: 1283.53068
MathSciNet: MR3080809

Subjects:
Primary: 20F16, 55P20, 55P62
Secondary: 22E40, 32J27

Rights: Copyright © 2013 Osaka University and Osaka City University, Departments of Mathematics

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Vol.50 • No. 2 • June 2013
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