English

Formality and hard Lefschetz property of aspherical manifolds

Geometric Topology 2012-03-08 v4

Abstract

For a Lie group G=RnϕRmG=\R^{n}\ltimes_{\phi}\R^{m} with the semi-simple action ϕ:RnAut(Rm)\phi:\R^{n}\to {\rm Aut}(\R^{m}), we show that if Γ\Gamma is a finite extension of a lattice of GG then K(Γ,1)K(\Gamma, 1) is formal. Moreover we show that a compact symplectic aspherical manifold with the fundamental group Γ\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.

Keywords

Cite

@article{arxiv.0910.1175,
  title  = {Formality and hard Lefschetz property of aspherical manifolds},
  author = {Hisashi Kasuya},
  journal= {arXiv preprint arXiv:0910.1175},
  year   = {2012}
}

Comments

14 pages to appear in Osaka J. Math