2019/12/10 by Hyungryul Baik, Baik, Hyungryul, KyeongRo Kim +1
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.GT
paper · pdf · doi:10.48550/arxiv.1912.04553
arxiv created 2019/12/10 · openalex publication_date 2019/12/10 · arxiv updated 2019/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Thurston showed that the fundamental group of a close atoroidal 3-manifold admitting a co-oriented taut foliation acts faithfully on the circle by orientation-preserving homeomorphisms. This action on the circle is called a universal circle action due to its rich information. In this article, we first review Thurston's theory of universal circles and follow-up work of other authors. We note that the universal circle action of a 3-manifold group always admits an invariant lamination. A group acting on the circle with an invariant lamination is called a laminar group. In the second half of the paper, we discuss the theory of laminar groups and prove some interesting properties of laminar groups under various conditions.