# Bott-Chern cohomology of solvmanifolds

created by daniele on 22 Jun 2016
modified on 27 Nov 2017

[BibTeX]

Published Paper

Inserted: 22 jun 2016
Last Updated: 27 nov 2017

Journal: Ann. Global Anal. Geom.
Volume: 52
Number: 4
Pages: 363-411
Year: 2017
Doi: 10.1007/s10455-017-9560-6

ArXiv: 1212.5708 PDF
We study conditions under which sub-complexes of a double complex of vector spaces allow to compute the Bott-Chern cohomology. We are especially aimed at studying the Bott-Chern cohomology of special classes of solvmanifolds, namely, complex parallelizable solvmanifolds and solvmanifolds of splitting type. More precisely, we can construct explicit finite-dimensional double complexes that allow to compute the Bott-Chern cohomology of compact quotients of complex Lie groups, respectively, of some Lie groups of the type $\mathbb{C}^n\ltimes_\varphi N$ where $N$ is nilpotent. As an application, we compute the Bott-Chern cohomology of the complex parallelizable Nakamura manifold and of the completely-solvable Nakamura manifold. In particular, the latter shows that the property of satisfying the $\partial\overline\partial$-Lemma is not strongly-closed under deformations of the complex structure.