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|Title:||The holonomy groupoids of singularly foliated bundles|
|Citation:||Symmetry, Integrability and Geometry: Methods and Applications, 2021; 17:043-1-043-34|
|Lachlan Ewen MacDonald|
|Abstract:||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.|
|Keywords:||Singular foliation; connection; holonomy; diffeology|
|Rights:||Copyright Status Unknown|
|Appears in Collections:||Aurora harvest 8|
Australian Institute for Machine Learning publications
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