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https://hdl.handle.net/2440/131404
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Type: | Journal article |
Title: | The holonomy groupoids of singularly foliated bundles |
Author: | MacDonald, L.E. |
Citation: | Symmetry, Integrability and Geometry: Methods and Applications, 2021; 17:043-1-043-34 |
Publisher: | SIGMA |
Issue Date: | 2021 |
ISSN: | 1815-0659 1815-0659 |
Statement of Responsibility: | 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 |
DOI: | 10.3842/sigma.2021.043 |
Grant ID: | http://purl.org/au-research/grants/arc/DP200100729 |
Published version: | http://dx.doi.org/10.3842/sigma.2021.043 |
Appears in Collections: | Aurora harvest 8 Australian Institute for Machine Learning publications |
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