Resilient leaves in transversely affine foliations (Q1121560)

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scientific article; zbMATH DE number 4104003
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Resilient leaves in transversely affine foliations
scientific article; zbMATH DE number 4104003

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    Resilient leaves in transversely affine foliations (English)
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    1989
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    \textit{P. Furness} and \textit{E. Fedida} [Glasg. Math. J. 17, 106-111 (1976; Zbl 0329.57004), Theorem 3] incorrectly asserted that a transversely affine foliation of codimension one cannot have exceptional leaves. In this paper a counterexample to their assertion is given on a closed 3- manifold. (It seems that a similar example was already known to \textit{G. Hector} (unpublished).) It is also shown that a transversely affine foliation of codimension one has locally dense resilient leaves if and only if its global holonomy group is non-abelian. This result contains Theorem 1 of \textit{P. Furness} and \textit{E. Fedida} [C. R. Acad. Sci. Paris, Ser. A 282, 825-827 (1976; Zbl 0321.57017)] as a special case.
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    transversely affine foliation of codimension one
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    exceptional leaves
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    locally dense resilient leaves
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    global holonomy group
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