Infinitely many hyperbolic 3-manifolds which contain no Reebless foliation

Roberts, R. ¹   ; Shareshian, J. ¹   ; Stein, M. ²

¹ Department of Mathematics, Washington University, St Louis, Missouri 63130
² Department of Mathematics, Trinity College, Hartford, Connecticut 06106

Journal of the American Mathematical Society, Tome 16 (2003) no. 3, pp. 639-679

Résumé

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 $\mathbb R$-order trees and hence these 3-manifolds contain no transversely oriented essential lamination; in particular, they are non-Haken.

Détail

DOI : 10.1090/S0894-0347-03-00426-0

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