Laminations and groups of homeomorphisms of the circle
Abstract
If M is an atoroidal 3-manifold with a taut foliation, Thurston showed that pi_1(M) acts on a circle. Here, we show that some other classes of essential laminations also give rise to actions on circles. In particular, we show this for tight essential laminations with solid torus guts. We also show that pseudo-Anosov flows induce actions on circles. In all cases, these actions can be made into faithful ones, so pi_1(M) is isomorphic to a subgroup of Homeo(S^1). In addition, we show that the fundamental group of the Weeks manifold has no faithful action on S^1. As a corollary, the Weeks manifold does not admit a tight essential lamination, a pseudo-Anosov flow, or a taut foliation. Finally, we give a proof of Thurston's universal circle theorem for taut foliations based on a new, purely topological, proof of the Leaf Pocket Theorem.
Keywords
Cite
@article{arxiv.math/0203192,
title = {Laminations and groups of homeomorphisms of the circle},
author = {Danny Calegari and Nathan M. Dunfield},
journal= {arXiv preprint arXiv:math/0203192},
year = {2015}
}
Comments
50 pages, 12 figures. Ver 2: minor improvements