Please use this identifier to cite or link to this item: 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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