Strong generalized holomorphic principal bundles
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913391069626368 |
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| author | Pal, Debjit Poddar, Mainak |
| author_facet | Pal, Debjit Poddar, Mainak |
| contents | We introduce the notion of a strong generalized holomorphic (SGH) fiber bundle and develop connection and curvature theory for an SGH principal $G$-bundle over a regular generalized complex (GC) manifold, where $G$ is a complex Lie group. We develop a de Rham cohomology for regular GC manifolds, and a Dolbeault cohomology for SGH vector bundles. Moreover, we establish a Chern-Weil theory for SGH principal $G$-bundles under certain mild assumptions on the leaf space of the GC structure. We also present a Hodge theory along with associated dualities and vanishing theorems for SGH vector bundles. Several examples of SGH fiber bundles are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18113 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strong generalized holomorphic principal bundles Pal, Debjit Poddar, Mainak Differential Geometry Complex Variables Symplectic Geometry Primary: 53D18, 32L05, 32L20. Secondary: 57R22, 57R30, 53D05 We introduce the notion of a strong generalized holomorphic (SGH) fiber bundle and develop connection and curvature theory for an SGH principal $G$-bundle over a regular generalized complex (GC) manifold, where $G$ is a complex Lie group. We develop a de Rham cohomology for regular GC manifolds, and a Dolbeault cohomology for SGH vector bundles. Moreover, we establish a Chern-Weil theory for SGH principal $G$-bundles under certain mild assumptions on the leaf space of the GC structure. We also present a Hodge theory along with associated dualities and vanishing theorems for SGH vector bundles. Several examples of SGH fiber bundles are given. |
| title | Strong generalized holomorphic principal bundles |
| topic | Differential Geometry Complex Variables Symplectic Geometry Primary: 53D18, 32L05, 32L20. Secondary: 57R22, 57R30, 53D05 |
| url | https://arxiv.org/abs/2404.18113 |