The Frolicher Spectral Sequence of Certain Solvmanifolds

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 = C-n infinity(phi) N of Lie groups with lattice Gamma = Gamma' infinity Gamma '' such that N is a nilpotent Lie group with a left-invariant complex structure and phi is a semi-simple action, we also show that, if the Frolicher spectral sequence of the nilmanifold N/Gamma '' is degenerate at the E-r -term for r >= 2, then the Frolicher spectral sequence of the solvmanifold G/Gamma is also degenerate at the E-r -term.