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arxiv: 2004.13929 · v2 · pith:H3HCXWF7new · submitted 2020-04-29 · 🧮 math.DG

Hierarchies of holonomy groupoids for foliated bundles

classification 🧮 math.DG
keywords holonomybundlefoliateddiffeologicalgroupoidgroupoidsassociatedbundles
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We give a new construction of the holonomy groupoid of a regular foliation in terms of a partial connection on a diffeological principal bundle of germs of transverse parametrisations. We extend these ideas to construct a novel holonomy groupoid for any foliated bundle, which we prove sits at the top of a hierarchy of diffeological jet holonomy groupoids associated to the foliated bundle.

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