Laminar Groups and 3-Manifolds

Hyungryul Baik () and KyeongRo Kim ()
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Hyungryul Baik: KAIST, Department of Mathematical Sciences
KyeongRo Kim: KAIST, Department of Mathematical Sciences

Chapter Chapter 10 in In the Tradition of Thurston, 2020, pp 365-421 from Springer

Abstract: Abstract Thurston showed that the fundamental group of a closed 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 the rich information it carries. In this chapter, 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 chapter, we discuss the theory of laminar groups and prove some interesting properties of laminar groups under various conditions.

Keywords: Tits alternative; Laminations; Circle homeomorphisms; Fuchsian groups; Fibered 3-manifolds; Pseudo-Anosov surface diffeomorphism; 20F65; 20H10; 37C85; 37E10; 57M60 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/978-3-030-55928-1_10

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