Dolbeault formality for complex nilmanifolds
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911447791960064 |
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| author | Sferruzza, Tommaso Verbitsky, Misha |
| author_facet | Sferruzza, Tommaso Verbitsky, Misha |
| contents | A quasi-isomorphism of differential graded algebras (DGA) is a multiplicative map inducing an isomorphism on cohomology. A DGA is called formal if it can be connected by a chain of quasi-isomorphisms to its cohomology algebra. We prove that the Dolbeault DGA of a complex nilmanifold is formal only if it is a torus, and the Dolbeault algebra of (0,p)-forms is formal if and only if the complex structure is abelian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13426 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dolbeault formality for complex nilmanifolds Sferruzza, Tommaso Verbitsky, Misha Differential Geometry Algebraic Topology A quasi-isomorphism of differential graded algebras (DGA) is a multiplicative map inducing an isomorphism on cohomology. A DGA is called formal if it can be connected by a chain of quasi-isomorphisms to its cohomology algebra. We prove that the Dolbeault DGA of a complex nilmanifold is formal only if it is a torus, and the Dolbeault algebra of (0,p)-forms is formal if and only if the complex structure is abelian. |
| title | Dolbeault formality for complex nilmanifolds |
| topic | Differential Geometry Algebraic Topology |
| url | https://arxiv.org/abs/2602.13426 |