2022/11/27 by Álvaro del Pino, del Pino, Álvaro, Aldo Witte +1
Mathematics · #53C12 #53D05 #53D10 #53D17 #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2211.14891
openalex publication_date 2022/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe a procedure, called regularisation, that allows us to study geometric structures on Lie algebroids via foliated geometric structures on a manifold of higher dimension. This procedure applies to various classes of Lie algebroids; namely, those whose singularities are of bk, complex-log, or elliptic type, possibly with self-crossings. One of our main applications is a proof of the Weinstein conjecture for overtwisted bk-contact structures. This was proven by Miranda-Oms using a certain technical hypothesis. Our approach avoids this assumption by reducing the proof to the foliated setting. As a by-product, we also prove the Weinstein conjecture for other Lie algebroids. Along the way we also introduce tangent distributions, i.e. subbundles of Lie algebroids, as interesting objects of study and present a number of constructions for them.