Laminations and groups of homeomorphisms of the circle
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.
If M is an atoroidal 3-manifold with a taut foliation, Thurston showed that π1(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 π1(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 with solid torus guts, 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.
- Laminations and groups of homeomorphisms of the circle
Volume 152, Issue 1 , pp 149-204
- Cover Date
- Print ISSN
- Online ISSN
- Additional Links
- Author Affiliations
- A1. Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, USA (e-mail: email@example.com), US
- A2. Department of Mathematics, Harvard University, Cambridge, MA 02138, USA (e-mail: firstname.lastname@example.org), US