Dolbeault cohomology for almost complex manifolds
This paper extends Dolbeault cohomology and its surrounding theory to arbitrary almost complex manifolds. We define a spectral sequence converging to ordinary cohomology, whose first page is the Dolbeault cohomology, and develop a harmonic theory which injects into Dolbeault cohomology. Lie-theoreti...
| Authors: | ; |
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| Format: | Article |
| Status: | Published version |
| Publication date: | 2021 |
| Country: | España |
| Institution: | Universidad de Barcelona |
| Repository: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/181976 |
| Online Access: | https://hdl.handle.net/2445/181976 |
| Access Level: | Open access |
| Keyword: | Varietats complexes Geometria diferencial global Homologia Complex manifolds Global differential geometry Homology |
| Summary: | This paper extends Dolbeault cohomology and its surrounding theory to arbitrary almost complex manifolds. We define a spectral sequence converging to ordinary cohomology, whose first page is the Dolbeault cohomology, and develop a harmonic theory which injects into Dolbeault cohomology. Lie-theoretic analogues of the theory are developed which yield important calculational tools for Lie groups and nilmanifolds. Finally, we study applications to maximally non-integrable manifolds, including nearly Kähler |
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