Daniele Angella

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

On Bott-Chern cohomology of compact complex surfaces

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

On the Chern–Yamabe problem

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

COHOMOLOGY OF D-COMPLEX MANIFOLDS

\partial \overline{\partial }

On small deformations of balanced manifolds

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

Locally Conformal Hermitian Metrics on Complex Non-Kähler Manifolds

Preliminaries on (almost-) complex manifolds.- Cohomology of complex manifolds.- Cohomology of nilmanifolds.- Cohomology of almost-complex manifolds.- References.