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arXiv · 2111.01032

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

Derek Krepski·Jordan Watts·Seth Wolbert
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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.

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Derek Krepski, Jordan Watts, Seth Wolbert. 2021-11-01. Sheaves, principal bundles, and \v{C}ech cohomology for diffeological spaces. https://arxiv.org/abs/2111.01032

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