奇异叶丛的整群胚
The Holonomy Groupoids of Singularly Foliated Bundles
摘要：
我们定义了一个概念的连接在一个纤维丛，是兼容的一个奇异的叶理的基础。配备有这种联系的纤维丛是丰富的供应，自然产生的任何李群-等变丛，并同时推广规则叶状丛的意义上的Kamber-Tondeur和奇异叶状。我们定义了层次的拓扑holonomy groupoid相关联的这样的束，这是从平行运输的喷气机/germinal守恒定律。我们表明，以这种方式关联到平凡的奇异叶状丛的群胚是Androulidakis-Skandalis holonomy群胚的子群，这与Androulidakis-Skandalis holonomy群胚在正则情况下相一致。最后，我们证明了我们所有的结构在适当的态射下的函性。
英文摘要：
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.
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