Laminar groups and 3-manifolds

Hyungryul Baik; KyeongRo Kim

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arXiv · 1912.04553

Laminar groups and 3-manifolds

Hyungryul Baik·KyeongRo Kim

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Abstract

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.

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BibTeX RIS

Hyungryul Baik, KyeongRo Kim. 2019-12-10. Laminar groups and 3-manifolds. https://arxiv.org/abs/1912.04553

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