Document Type
Article
Department
​Mathematics
Publication Date
3-2003
Abstract
We investigate group actions on simply-connected (second countable but not necessarily Hausdorff) 1-manifolds and describe an infinite family of closed hyperbolic 3-manifolds whose fundamental groups do not act nontrivially on such 1-manifolds. As a corollary we conclude that these 3-manifolds contain no Reebless foliation. In fact, these arguments extend to actions on oriented -order trees and hence these 3-manifolds contain no transversely oriented essential lamination; in particular, they are non-Haken.
Comments
Originally published in JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY Volume 16, Number 3, Pages 639-679.
S 0894-0347(03)00426-0
http://www.ams.org/journals/jams/2003-16-03/S0894-0347-03-00426-0/home.html
Provided by the Trinity College Digital Repository in accordance with the publisher's archiving policies.