The Frölicher spectral sequence of certain solvmanifolds

Abstract

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 $\Gamma ={\Gamma }^{\prime }⋉{\Gamma }^{\prime \prime }$ such that $N$ is a nilpotent Lie-group with a left-invariant complex structure and $\varphi$ is a semi-simple action, we also show that, if the Frölicher spectral sequence of the nilmanifold $N/{\Gamma }^{\prime \prime }$ is degenerate at $E_r$-term for $r\ge 2$, then the Frölicher spectral sequence of the solvmanifold $G/\Gamma$ is also degenerate at $E_r$-term.

arXiv commentTo appear in J. Geom. Anal

References in corpus (1)

• de Rham and Dolbeault Cohomology of solvmanifolds with local systems