Intersection of transverse foliations in 3-manifolds: Hausdorff leafspace implies leafwise quasi-geodesic

2023/10/08 by Sérgio R. Fenley, Fenley, Sergio R., Rafaël Potrie +1 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2310.05176

openalex publication_date 2023/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F₁ and F₂ be transverse two dimensional foliations with Gromov hyperbolic leaves in a closed 3-manifold M whose fundamental group is not solvable, and let G be the one dimensional foliation obtained by intersection. We show that G is leafwise quasigeodesic in F₁ and F₂ if and only if the foliation G_L induced by G in the universal cover L of any leaf of F₁ or F₂ has Hausdorff leaf space. We end up with a discussion on the hypothesis of Gromov hyperbolicity of the leaves.

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• Partially hyperbolic diffeomorphisms homotopic to the identity in dimension three

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