The Frölicher spectral sequence of certain solvmanifolds (Q2256836)

Let \(N\) be a complex simply connected parallelizable nilpotent Lie group. Let \(\phi\) be a semisimple action of \(\mathbb {C}^n\) on \(N\). The corresponding semidirect product \(G = \mathbb {C}^n \ltimes_\phi N\) is a solvmanifold. For example \(G\) can be the Borel subgroup of a complex semisimple Lie group with Cartan subgroup \(\mathbb {C}^n\). Consider a lattice \(\Gamma = \Gamma' \ltimes \Gamma''\) of \(G\). The article shows that if the Frölicher spectral sequence of \(N/\Gamma''\) is degenerate at the \(E_r\)-term for \(r \geq 2\), then the Frölicher spectral sequence of \(G/\Gamma\) is also degenerate at the \(E_r\)-term.