Leaf topology of minimal hyperbolic foliations with non simply-connected generic leaf

2022/06/22 by Paulo Gusmão, Gusmão, Paulo, Carlos Meniño Cotón +1
Mathematics · #57R30 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2206.10970

openalex publication_date 2022/06/22 · openalex created_date 2023/02/13 · openalex updated_date 2026/08/01

Abstract

A noncompact (oriented) surface satisfies the condition (⋆) if their isolated ends are ''accumulated by genus''. We show that every surface satisfying this condition is homeomorfic to the leaf of a minimal codimension one foliation on a closed 3-manifold whose generic leaf is not simply connected. Moreover, the above result is also true for any prescription of a countable family of noncompact surfaces (satisfying (⋆)): they can coexist in the same minimal codimension one foliation as above. All the given examples are hyperbolic foliations, meaning that they admit a leafwise Riemannian metric of constant negative curvature.

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