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An invitation to singular foliations

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arxiv 2407.14932 v2 pith:2ZQUJ3EY submitted 2024-07-20 math.DG

Camille Laurent-Gengoux , Ruben Louis , Leonid Ryvkin This is my paper · ORCID
classification math.DG
keywords attemptfoliationsseveralsingularvariousadditionandroulidakisconstructions
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Blowups of Dirac structures

    math.SG 2025-06 accept novelty 8.0 of 10

    A Dirac structure lifts to the real projective blowup exactly for transverse submanifolds or invariant submanifolds whose transverse Lie algebras have constant height 0 or 1, classified as abelian, R semidirect R^n, or so(3).

  2. Carrollian Lie Algebroids: Taming Singular Carrollian Geometries

    math.DG 2025-10 conditional novelty 6.0 of 10

    Carrollian Lie algebroids extend Carrollian geometry to allow Carroll vector fields with zeros, encode the singularities in the anchor map, and always admit Carrollian (compatible) connections.

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