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PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
 

Summary: PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 126, Number 3, March 1998, Pages 925931
S 0002-9939(98)04225-7
FOLIATIONS OF SOME 3-MANIFOLDS
WHICH FIBER OVER THE CIRCLE
D. COOPER AND D. D. LONG
(Communicated by Ronald A. Fintushel)
Abstract. We show that a hyperbolic punctured torus bundle admits a foli-
ation by lines which is covered by a product foliation. Thus its fundamental
group acts freely on the plane.
1. Introduction
This paper discusses one dimensional foliations of closed three-manifolds. Every
closed three-manifold admits a one dimensional foliation; for example the three-
sphere admits a foliation by round circles (Hopf) and by smooth lines [4]. Epstein,
[3], showed that every foliation by circles is a Seifert fibration, and this class of
manifolds has been extensively studied. A manifold which fibers over the circle
admits a one dimensional foliation such that each leaf maps monotonely under the
map to the circle defining the fibration. If a closed three-manifold admits one of
the eight geometric structures described by Thurston, [5], then it is either Seifert

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics