 
Summary: PROCEEDINGS OF THE
AMERICAN MATHEMATICAL SOCIETY
Volume 126, Number 3, March 1998, Pages 925931
S 00029939(98)042257
FOLIATIONS OF SOME 3MANIFOLDS
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 threemanifolds. Every
closed threemanifold 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 threemanifold admits one of
the eight geometric structures described by Thurston, [5], then it is either Seifert
