Techniques of computations of Dolbeault cohomology of solvmanifolds

By H. Kasuya. 2011

52 citations recorded by the source corpus.

We consider semi-direct products $${\mathbb{C}^{n}\ltimes_{\phi}N}$$ of Lie groups with lattices Γ such that N are nilpotent Lie groups with left-invariant complex structures. We compute the Dolbeault cohomology of direct sums of holomorphic line bundles over G/Γ by using the Dolbeaut cohomology of the Lie algebras of the direct product $${\mathbb{C}^{n}\times N}$$ . As a corollary of this computation, we can compute the Dolbeault cohomology Hp,q(G/Γ) of G/Γ by using a finite dimensional cochain complexes. Computing some examples, we observe that the Dolbeault cohomology varies for choices of lattices Γ.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7594cf5395ff6d1c75a0298a56203ca3e7852918

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In Applied Mathematics

1. Daniele Angella
2. H. Kasuya
3. J. Stelzig

In Geometry and Topology

1. Daniele Angella
2. H. Kasuya
3. J. Stelzig

In Mathematical Physics

1. Daniele Angella
2. H. Kasuya
3. J. Stelzig

Citations in the corpus

• The Cohomologies of the Iwasawa Manifold and of Its Small Deformations (2012, result): “ also for the Dolbeault cohomology, see, e.g., [5] and [24] for surveys on the known results. (Some results about the Dolbeault cohomology of solvmanifolds have been recently proved by H. Kasuya, see [14].) Theorem 2.3 ([25, Theorem 1], [8, Main Theorem], [6, Theorem 2, Remark 4], [22, Theorem 1.10]”
• Bott–Chern cohomology of solvmanifolds (2012, background): “In [40], it is shown that for some left-invariant Hermitian metric the space of harmonic forms admits the Hodge decomposition and symmetry (see also [41] for higher dimensional examples with the Hodge decomposition and symmetry).”