Minimality of the action on the universal circle of uniform foliations

IF 0.6 3区数学 Q3 MATHEMATICS

Groups Geometry and Dynamics Pub Date : 2020-01-15 DOI:10.4171/ggd/637

Sérgio R. Fenley, R. Potrie

引用次数: 6

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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均匀叶形万向圆上作用的极小性

给出了$3$流形上的Gromov双曲叶的一致叶化，证明了基本群在万圆上的作用在不同点对上是极小的和可传递的。我们还证明了另外两个结果:证明了一般的一致无reeless叶是$\mathbb{R}$-覆盖的，并利用$M$的JSJ分解给出了$\mathbb{R}$-覆盖的具有Gromov双曲叶的叶的普遍圆的新描述。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Groups Geometry and Dynamics 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Groups, Geometry, and Dynamics is devoted to publication of research articles that focus on groups or group actions as well as articles in other areas of mathematics in which groups or group actions are used as a main tool. The journal covers all topics of modern group theory with preference given to geometric, asymptotic and combinatorial group theory, dynamics of group actions, probabilistic and analytical methods, interaction with ergodic theory and operator algebras, and other related fields. Topics covered include: geometric group theory; asymptotic group theory; combinatorial group theory; probabilities on groups; computational aspects and complexity; harmonic and functional analysis on groups, free probability; ergodic theory of group actions; cohomology of groups and exotic cohomologies; groups and low-dimensional topology; group actions on trees, buildings, rooted trees.