Hierarchies of holonomy groupoids for foliated bundles
Differential Geometry
2021-02-11 v2
Abstract
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.
Keywords
Cite
@article{arxiv.2004.13929,
title = {Hierarchies of holonomy groupoids for foliated bundles},
author = {Lachlan Ewen MacDonald},
journal= {arXiv preprint arXiv:2004.13929},
year = {2021}
}
Comments
40 pages, minor editing changes