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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A condition for the stability of $\mathbb{R} $-covered on foliations of 3-manifolds


Authors: Sue Goodman and Sandi Shields
Journal: Trans. Amer. Math. Soc. 352 (2000), 4051-4065
MSC (2000): Primary 57M12, 57M20, 57N10, 57R30
Published electronically: May 12, 2000
MathSciNet review: 1624178
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Abstract: We give a sufficient condition for a codimension one, transversely orientable foliation of a closed 3-manifold to have the property that any foliation sufficiently close to it be $\mathbb{R} $-covered. This condition can be readily verified for many examples. Further, if an $\mathbb{R} $-covered foliation has a compact leaf $L$, then any transverse loop meeting $L$ lifts to a copy of the leaf space, and the ambient manifold fibers over $S^1$ with $L$ as fiber.


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Additional Information

Sue Goodman
Affiliation: Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3902
Email: seg@math.unc.edu

Sandi Shields
Affiliation: Department of Mathematics, College of Charleston, Charleston, South Carolina 29424
Email: shields@math.cofc.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02391-6
PII: S 0002-9947(00)02391-6
Keywords: Branched surface, foliation, $\mathbb{R}$-covered
Received by editor(s): September 3, 1996
Received by editor(s) in revised form: April 18, 1998
Published electronically: May 12, 2000
Article copyright: © Copyright 2000 American Mathematical Society