Bott–Chern cohomology of solvmanifolds
By Daniele Angella, H. Kasuya. 2012
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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 $$\mathbb {C}^n\ltimes _\varphi N$$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 $$\partial \overline{\partial }$$∂∂¯-Lemma is not strongly closed under deformations of the complex structure.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/a535876583f1e1d5b8f45c457119bee0f3a323a8
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- On the structure of double complexes (2018, background): “In particular, one immediately recovers the following fact (see also [4], [7], for previous special cases): Corollary 13.”