Formality and hard Lefschetz property of aspherical manifolds

Details Formality and hard Lefschetz property of aspherical manifolds Formality and hard Lefschetz property of aspherical manifolds

2009-10-07

arxiv.org/abs/0910.1175v4

Mathematics

Geometric Topology

14 pages to appear in Osaka J. Math

Scientific paper

For a Lie group $G=\R^{n}\ltimes_{\phi}\R^{m}$ with the semi-simple action $\phi:\R^{n}\to {\rm Aut}(\R^{m})$, 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 K\"ahler structures.

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