论文标题
奇异叶捆的尸体类型
The Holonomy Groupoids of Singularly Foliated Bundles
论文作者
论文摘要
我们在纤维捆绑包中定义了连接的概念，该概念与底座的奇异叶子兼容。配备了这种连接的纤维捆绑包有充足的供应，自然而然地是针对任何子类固定套件的捆绑包，同时在kamber-tondeur和奇异叶子的意义上同时概括了定期叶的捆绑包。我们定义了与此类束相关的差异尸体类别的层次结构，这是由喷气/发芽保护法的平行运输产生的。我们表明，以这种方式与琐碎的奇异叶束相关的类固醇是Androulidakis-skandalis固有类的商，它们与常规案例中的Androulidakis-Skandalis固有类别相吻合。最后，我们证明了在适当的形态下我们所有结构的功能。
We define a notion of connection in a fibre bundle that is compatible with a singular foliation of the base. Fibre bundles equipped with such connections are in plentiful supply, arising naturally for any Lie groupoid-equivariant bundle, and simultaneously generalising regularly foliated bundles in the sense of Kamber-Tondeur and singular foliations. We define hierarchies of diffeological holonomy groupoids associated to such bundles, which arise from the parallel transport of jet/germinal conservation laws. We show that the groupoids associated in this manner to trivial singularly foliated bundles are quotients of Androulidakis-Skandalis holonomy groupoids, which coincide with Androulidakis-Skandalis holonomy groupoids in the regular case. Finally we prove functoriality of all our constructions under appropriate morphisms.
