Laminations and groups of homeomorphisms of the circle

Danny Calegari, Nathan M. Dunfield

Research output: Contribution to journalArticlepeer-review

Abstract

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(S1). In addition, we show that the fundamental group of the Weeks manifold has no faithful action on S1. 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.

Original languageEnglish (US)
Pages (from-to)149-204
Number of pages56
JournalInventiones Mathematicae
Volume152
Issue number1
DOIs
StatePublished - 2003
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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