Local coordinates for non-integrable Lie algebroids constructed.
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problem Constructing local coordinates for non-integrable Lie algebroids.
method Reformulating bi-submersion algebraically and proving their existence for the Weinstein groupoid.
result Existence of -algebra attached to every Lie algebroid.
Constructs a Lie groupoid integrating singular foliations.
problem Integrating singular foliations into higher Lie groupoids.
method Recursive use of bi-submersions and geometric resolutions.
result Finite-dimensional Lie groupoid integrating singular foliations.
We construct the holonomy groupoid of any singular foliation. In the regular case this groupoid coincides with the usual holonomy groupoid of Winkelnkemper (1983); the same holds in the singular cases of Bigonnet and Pradines (1985) and Debord (2001), which from our point of view can be thought of as being "almost regu…
Paper studies symmetries in singular foliations using Lie -morphisms.
problem Understanding symmetries in singular foliations.
method Analyzes Lie -morphisms induced by Lie algebra actions on singular foliations.
result Deduces geometrical consequences, including examples of non-extendable symmetries.
This research extends Lie algebra actions to singular foliations.
problem Understanding symmetries in singular foliations without additional assumptions.
method Equivalence of categories between Lie-Rinehart algebras and Lie -algebroids.
result Universal Lie -algebroids for singular foliations.