Hisashi Kasuya

Bott–Chern cohomology of solvmanifolds

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

The Frölicher Spectral Sequence of Certain Solvmanifolds

\mathbb {C}^n\ltimes _\varphi N

Transverse Kähler structures on central foliations of complex manifolds

Cn⋉φN 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

ON DE RHAM AND DOLBEAULT COHOMOLOGY OF SOLVMANIFOLDS

\partial \overline{\partial }

An extention of Nomizu’s Theorem –A user’s guide–

∂∂¯-Lemma is not strongly closed under deformations of the complex structure.

Examples of Non-Kähler Solvmanifolds Admitting Hodge Decomposition

Abstract We study cohomologies and Hodge theory for complex manifolds with twisted differentials. In particular, we get another cohomological obstruction for manifolds in class C of Fujiki. We give a Hodgetheoretical proof of the characterization of solvmanifolds in class C of Fujiki, first stated by D. Arapura.