Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Formality and hard Lefschetz property of aspherical manifolds   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.

34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc