Laminar groups and 3-manifolds
Geometric Topology
2019-12-11 v1
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.
Cite
@article{arxiv.1912.04553,
title = {Laminar groups and 3-manifolds},
author = {Hyungryul Baik and KyeongRo Kim},
journal= {arXiv preprint arXiv:1912.04553},
year = {2019}
}