The Atiyah class of generalized holomorphic vector bundles

2021/02/14 by Honglei Lang, Xiao Jia, Lang, Honglei +3 · 2 citations
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Geometry and complex manifolds #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2102.07177

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 Čech cohomology, using the first-jet short exact sequence, or adopting the Lie pair point of view.

Cited by

• Atiyah Classes in the Context of Generalized Complex Geometry
• Atiyah constructions for Lie algebroid connections on fiber bundles

Related

• Atiyah Classes in the Context of Generalized Complex Geometry
• Atiyah's work on holomorphic vector bundles and gauge theories
• Atiyah constructions for Lie algebroid connections on fiber bundles
• On connections on principal bundles
• On the obstruction to extending a vector bundle from a submanifold