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https://hdl.handle.net/2440/131404
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DC Field | Value | Language |
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dc.contributor.author | MacDonald, L.E. | - |
dc.date.issued | 2021 | - |
dc.identifier.citation | Symmetry, Integrability and Geometry: Methods and Applications, 2021; 17:043-1-043-34 | - |
dc.identifier.issn | 1815-0659 | - |
dc.identifier.issn | 1815-0659 | - |
dc.identifier.uri | http://hdl.handle.net/2440/131404 | - |
dc.description.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. | - |
dc.description.statementofresponsibility | Lachlan Ewen MacDonald | - |
dc.language.iso | en | - |
dc.publisher | SIGMA | - |
dc.rights | Copyright Status Unknown | - |
dc.source.uri | http://dx.doi.org/10.3842/sigma.2021.043 | - |
dc.subject | Singular foliation; connection; holonomy; diffeology | - |
dc.title | The holonomy groupoids of singularly foliated bundles | - |
dc.type | Journal article | - |
dc.identifier.doi | 10.3842/sigma.2021.043 | - |
dc.relation.grant | http://purl.org/au-research/grants/arc/DP200100729 | - |
pubs.publication-status | Published | - |
dc.identifier.orcid | MacDonald, L.E. [0000-0003-3601-9777] | - |
Appears in Collections: | Aurora harvest 8 Australian Institute for Machine Learning publications |
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