Leafwise Quasigeodesic Foliation in Dimension Three and the Funnel Property

2021/05/12 by Chanda, Anindya, Fenley, Sergio
#37C15 #37D10 #37D20 #37D45 #53C23. Secondary:37D40 #57R30 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Primary: 37C10

paper · doi:10.48550/arxiv.2105.05430

Abstract

We construct one dimensional foliations which are subfoliations of two dimensional foliations in 3-manifolds. The subfoliation is by quasigeodesics in each two dimensional leaf, but it is not funnel: not all quasigeodesics share a common ideal point in most leaves. This article answers the question whether the funnel property is a consequence of the leafwise quasigeodesic property or not.

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