abstract: These lecture notes attempt to invite the reader towards the theory of singular foliations, both smooth and holomorphic. In addition to a systematic review of the foundations, and an attempt to put in order examples and several elementary constructions, we detail several recent tools developed for non-commutative geometry, in particular the holonomy groupoid of Androulidakis and Skandalis and various methods for resolving singularities. We also introduce various homotopic notions, and end with a series of open questions.

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@book{Laurent-Gengoux-An-invitation-to-2024,
 abstract = {These lecture notes attempt to invite the reader towards the theory of
singular foliations, both smooth and holomorphic. In addition to a systematic
review of the foundations, and an attempt to put in order examples and several
elementary constructions, we detail several recent tools developed for
non-commutative geometry, in particular the holonomy groupoid of Androulidakis
and Skandalis and various methods for resolving singularities. We also
introduce various homotopic notions, and end with a series of open questions.},
 arxiv = {arXiv:2407.14932},
 author = {Laurent-Gengoux, Camille and Louis, Ruben and Ryvkin, Leonid},
 eprint = {2407.14932},
 howpublished = {Preprint, {arXiv}:2407.14932 [math.{DG}] (2024)},
 keywords = {53C12,32M25,32S50,22A22},
 publisher = {Accepted for publication in the Poisson geometry CRM Barcelona 2022 Springer booklet series},
 title = {An invitation to singular foliations},
 url = {https://arxiv.org/abs/2407.14932},
 year = {2024}
}