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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
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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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