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Sheaves, principal bundles, and \v{C}ech cohomology for diffeological spaces

Year: 2021

Type: preprint

Abstract: The purpose of this note is to define sheaves for diffeological spaces and give a construction of their \v{C}ech cohomology. As an application, we prove that the first degree \v{C}ech cohomology classes for the sheaf of smooth functions to an abelian diffeological group $G$ classify the diffeological principal $G$-bundles.

Source: arXiv (Cornell University)

Authors: Derek Krepski, Jordan Watts, Seth Wolbert

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W3208484635

Cites: 6

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Related to: 20