The Frölicher Spectral Sequence of Certain Solvmanifolds

Abstract

We show that the Frolicher spectral sequence of a complex parallelizable solvmanifold is degenerate at the E 2-term. For a semi-direct product $G=\mathbb{C}^{n}\ltimes_{\phi}N$ of Lie groups with lattice Γ=Γ′⋉Γ′′ such that N is a nilpotent Lie group with a left-invariant complex structure and ϕ is a semi-simple action, we also show that, if the Frolicher spectral sequence of the nilmanifold N/Γ′′ is degenerate at the E r -term for r≥2, then the Frolicher spectral sequence of the solvmanifold G/Γ is also degenerate at the E r -term.