Remarks on some compact symplectic solvmanifolds

TL;DR

This paper investigates the hard Lefschetz property on compact symplectic solvmanifolds, which are quotients of solvable Lie groups by lattices, focusing on their symplectic and topological characteristics.

Contribution

It provides new insights into the conditions under which compact symplectic solvmanifolds satisfy the hard Lefschetz property.

Findings

Identification of criteria for the hard Lefschetz property on these manifolds

Examples of symplectic solvmanifolds satisfying or failing the property

Connections between Lie group structure and symplectic topology

Abstract

We study the hard Lefschetz property on compact symplectic solvmanifolds, i.e., compact quotients $M=\Gamma\backslash G$ of a simply-connected solvable Lie group $G$ by a lattice $\Gamma$, admitting a symplectic structure.