微分论域上的层、主丛与 \v{C}ech 上同调
微分几何
2022-09-27 v2 代数拓扑
摘要
本注记旨在为微分论域（diffeological spaces）定义层，并给出其 \v{C}ech 上同调的构造。作为一个应用，我们证明了对到阿贝尔微分论域群 的光滑函数层而言，一阶 \v{C}ech 上同调类分类了微分论域主 -丛。
引用
@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}
}
备注
28 pages; v2: besides minor corrections and additions, we also added a subsection comparing this cohomology with that of Iglesias-Zemmour