Minimality of the action on the universal circle of uniform foliations

Sergio Fenley; Rafael Potrie

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arXiv · 2001.05522

Minimality of the action on the universal circle of uniform foliations

Sergio Fenley·Rafael Potrie

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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 $\mathbb{R}$-covered and we give a new description of the universal circle of $\mathbb{R}$-covered foliations with Gromov hyperbolic leaves in terms of the JSJ decomposition of $M$.

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Sergio Fenley, Rafael Potrie. 2020-01-15. Minimality of the action on the universal circle of uniform foliations. https://arxiv.org/abs/2001.05522

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