The Frölicher spectral sequence of certain solvmanifolds

We show that the Frölicher spectral sequence of a complex parallelizable solvmanifold is degenerate at $E_{2}$-term. For a semi-direct product $G=\C^{n}\ltimes_ϕN$ of Lie-groups with lattice $Γ=Γ^{\prime}\ltimes Γ^{\prime\prime}$ 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 Frölicher spectral sequence of the nilmanifold $N/Γ^{\prime\prime}$ is degenerate at $E_{r}$-term for $r\ge 2$, then the Frölicher spectral sequence of the solvmanifold $G/Γ$ is also degenerate at $E_{r}$-term.

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