Atiyah Classes in the Context of Generalized Complex 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.

Publication Details

Journal
ArXiv.org
Published
2025-08-14
Primary Topic
Homotopy and Cohomology in Algebraic Topology
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article

Atiyah Classes in the Context of Generalized Complex Geometry

ArXiv.org
Homotopy and Cohomology in Algebraic Topology
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Atiyah Classes in the Context of Generalized Complex Geometry

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Abstract

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.

ArXiv.org
Reduced inequalities
Openalex Percentile: Top 46%
Homotopy and Cohomology in Algebraic Topology
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Atiyah Classes in the Context of Generalized Complex Geometry · ArXiv.org (2025) | TGRS Research Map | TGRS