Atiyah Classes in the Context of Generalized Complex Geometry
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916899416178688 |
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| author | Ni, Dadi |
| author_facet | Ni, Dadi |
| contents | In analogy to the classical holomorphic setting, Lang, Jia and Liu introduced the notion of the Atiyah class for a generalized holomorphic vector bundle using three different approaches: leveraging $\rm{\check{C}}$ech cohomology, employing the first jet short exact sequence, and adopting the perspective of Lie algebroid pairs. The purpose of this note is to establish the equivalence among these diverse definitions of the Atiyah class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10723 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Atiyah Classes in the Context of Generalized Complex Geometry Ni, Dadi Differential Geometry In analogy to the classical holomorphic setting, Lang, Jia and Liu introduced the notion of the Atiyah class for a generalized holomorphic vector bundle using three different approaches: leveraging $\rm{\check{C}}$ech cohomology, employing the first jet short exact sequence, and adopting the perspective of Lie algebroid pairs. The purpose of this note is to establish the equivalence among these diverse definitions of the Atiyah class. |
| title | Atiyah Classes in the Context of Generalized Complex Geometry |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2508.10723 |