论文标题
$ b $ - 接触结构的存在和分类
Existence and classification of $b$-contact structures
论文作者
论文摘要
A $ b $ - 连接结构在$ b $ -manifold $（m，z）$上是$ m $上的雅各比结构，满足了沿Hypersurface $ z $的横向条件。我们表明，在三个维度上，具有$ b $的连接结构具有明显的三维叶子满足存在$ h $ - 原文，该结构允许开处方诱导的奇异叶面。我们提供了一种在给定的$ b $ manifold上对$ b $ - 接触结构进行分类的方法，并用它将$ s^3 $分类与两个尖峰或未结开的圆环作为关键表面。我们还讨论了更高维度的概括。
A $b$-contact structure on a $b$-manifold $(M,Z)$ is a Jacobi structure on $M$ satisfying a transversality condition along the hypersurface $Z$. We show that, in three dimensions, $b$-contact structures with overtwisted three-dimensional leaves satisfy an existence $h$-principle that allows prescribing the induced singular foliation. We give a method to classify $b$-contact structures on a given $b$-manifold and use it to give a classification on $S^3$ with either a two-sphere or an unknotted torus as the critical surface. We also discuss generalizations to higher dimensions.
