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

 

The stability of foliations
of orientable 3-manifolds
covered by a product


Author: Sandra L. Shields
Journal: Trans. Amer. Math. Soc. 348 (1996), 4653-4671
MSC (1991): Primary 57M12, 57M20, 57N10, 57R30, 58F10
MathSciNet review: 1355076
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Abstract | References | Similar Articles | Additional Information

Abstract: We examine the relationship between codimension one foliations that are covered by a trivial product of hyperplanes and the branched surfaces that can be constructed from them. We present a sufficient condition on a branched surface constructed from a foliation to guarantee that all $C^1$ perturbations of the foliation are covered by a trivial product of hyperplanes. We also show that a branched surface admits a strictly positive weight system if and only if it can be constructed from a fibration over $S^1$.


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Additional Information

Sandra L. Shields
Affiliation: Department of Mathematics, College of Charleston, Charleston, South Carolina 29424

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01631-5
PII: S 0002-9947(96)01631-5
Keywords: Branched surface, foliation, leaf space, holonomy map, topological equivalency
Received by editor(s): February 5, 1993
Received by editor(s) in revised form: October 9, 1995
Article copyright: © Copyright 1996 American Mathematical Society