奇异性叶状结构的爆破群胚
微分几何
2022-01-25 v2 算子代数
摘要
我们引入了在 Stefan 与 Sussmann 意义下任意奇异性叶状结构的光滑流形沿其奇异叶的爆破构造，以及由 Androulidakis 与 Skandalis 定义的完整群胚的爆破构造。我们的构造给出一个局部紧局部 Hausdorff 的群胚，可视为该奇异性叶状结构的去奇异化。我们证明其保留某些光滑结构。
引用
@article{arxiv.2105.05201,
title = {Blow-up groupoid of singular foliations},
author = {Omar Mohsen},
journal= {arXiv preprint arXiv:2105.05201},
year = {2022}
}
备注
Changed the title, abstract, introduction. I also added more details to the proofs, and in some cases simplified the proofs. Section 3 is new to this version. Lichnerowicz's formula is no longer the main motivation of the article