Sheaves, principal bundles, and \v{C}ech cohomology for diffeological spaces
Differential Geometry
2022-09-27 v2 Algebraic Topology
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 classify the diffeological principal -bundles.
Keywords
Cite
@article{arxiv.2111.01032,
title = {Sheaves, principal bundles, and \v{C}ech cohomology for diffeological spaces},
author = {Derek Krepski and Jordan Watts and Seth Wolbert},
journal= {arXiv preprint arXiv:2111.01032},
year = {2022}
}
Comments
28 pages; v2: besides minor corrections and additions, we also added a subsection comparing this cohomology with that of Iglesias-Zemmour