A condition for the stability of -covered on foliations of 3-manifolds |
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Authors: | Sue Goodman Sandi Shields |
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Institution: | Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3902 ; Department of Mathematics, College of Charleston, Charleston, South Carolina 29424 |
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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 -covered. This condition can be readily verified for many examples. Further, if an -covered foliation has a compact leaf , then any transverse loop meeting lifts to a copy of the leaf space, and the ambient manifold fibers over with as fiber. |
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Keywords: | Branched surface foliation $\mathbb{R}$-covered |
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