The Atiyah class of generalized holomorphic vector bundles
Honglei Lang, Xiao Jia, Zhangju Liu

TL;DR
This paper introduces the Atiyah class for generalized holomorphic vector bundles, providing a cohomological obstruction measure for the existence of generalized holomorphic connections, extending classical concepts to a broader geometric context.
Contribution
It defines the Atiyah class in three different frameworks for generalized holomorphic vector bundles, broadening the understanding of their geometric and cohomological properties.
Findings
Defines Atiyah class via Čech cohomology
Establishes Atiyah class using first-jet sequence
Adopts Lie pair perspective for Atiyah class
Abstract
We introduce the notion of Atiyah class of a generalized holomorphic vector bundle, which captures the obstruction to the existence of generalized holomorphic connections on the bundle. As in the classical holomorphic case, this Atiyah class can be defined in three different ways: using \v{C}ech cohomology, using the first-jet short exact sequence, or adopting the Lie pair point of view.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometry and complex manifolds · Advanced Algebra and Geometry
