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Foliations of some 3-manifolds which fiber over the circle
Author(s):
D.
Cooper;
D.
D.
Long
Journal:
Proc. Amer. Math. Soc.
126
(1998),
925-931.
MSC (1991):
Primary 57M50, 57M60, 57R30
MathSciNet review:
1443821
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Abstract:
We show that a hyperbolic punctured torus bundle admits a foliation by lines which is covered by a product foliation. Thus its fundamental group acts freely on the plane.
References:
- 1.
- A.F. Beardon The Geometry of Discrete Groups. Graduate Texts in Math. 91 (1983), Springer-Verlag. MR 85d:22026
- 2.
- D. Cooper, D.D. Long & A.W. Reid Essential closed surfaces in bounded 3-manifolds. J. Amer. Math. Soc. 10 (1997), no. 3, 553-563.
- 3.
- D.B.A. Epstein Periodic flows on three-dimensional manifolds. Ann. of Math. 95(1972), 66-82. MR 44:5981
- 4.
- K. Kuperberg A smooth counterexample to the Seifert conjecture. Ann. of Math. 140 (1994), no. 3, 723-732. MR 95g:57040
- 5.
- G.P. Scott The Geometries of 3-Manifolds. Bull. London Math. Soc. 15(1983), 401-487 MR 84m:57009
- 6.
- J. Stallings On Fibering certain 3-manifolds. Topology of 3-manifolds. 95-100, Prentice Hall (1962) MR 28:1600
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Additional Information:
D.
Cooper
Affiliation:
Department of Mathematics, University of California, Santa Barbara, California 93106
Email:
cooper@math.ucsb.edu
D.
D.
Long
Affiliation:
Department of Mathematics, University of California, Santa Barbara, California 93106
Email:
long@math.ucsb.edu
DOI:
10.1090/S0002-9939-98-04225-7
PII:
S 0002-9939(98)04225-7
Keywords:
$3$-manifold,
foliation,
product-covered,
surface-bundle
Received by editor(s):
June 16, 1996
Received by editor(s) in revised form:
September 4, 1996
Additional Notes:
Both authors was supported in part by NSF
Communicated by:
Ronald A. Fintushel
Copyright of article:
Copyright
1998,
American Mathematical Society
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