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A condition for the stability of -covered on foliations of 3-manifolds
Authors:Sue Goodman  Sandi Shields
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
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.

Keywords:Branched surface  foliation  $\mathbb{R}$-covered
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