Minimality of the action on the universal circle of uniform foliations

2020/01/15 by Fenley, Sergio, Potrie, Rafael · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2001.05522

Abstract

Given a uniform foliation by Gromov hyperbolic leaves on a 3-manifold, we show that the action of the fundamental group on the universal circle is minimal and transitive on pairs of different points. We also prove two other results: we prove that general uniform Reebless foliations are ℝ-covered and we give a new description of the universal circle of ℝ-covered foliations with Gromov hyperbolic leaves in terms of the JSJ decomposition of M.

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• Partially hyperbolic diffeomorphisms homotopic to the identity in dimension three

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