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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2012, Volume 278, Pages 102–113
(Mi tm3405)
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This article is cited in 1 scientific paper (total in 1 paper)
Compact leaves of structurally stable foliations
N. I. Zhukova Lobachevsky State University of Nizhni Novgorod, Nizhni Novgorod, Russia
Abstract:
We prove that any compact manifold whose fundamental group contains an abelian normal subgroup of positive rank can be represented as a leaf of a structurally stable suspension foliation on a compact manifold. In this case, the role of a transversal manifold can be played by an arbitrary compact manifold. We construct examples of structurally stable foliations that have a compact leaf with infinite solvable fundamental group which is not nilpotent. We also distinguish a class of structurally stable foliations each of whose leaves is compact and locally stable in the sense of Ehresmann and Reeb.
Received in March 2011
Citation:
N. I. Zhukova, “Compact leaves of structurally stable foliations”, Differential equations and dynamical systems, Collected papers, Trudy Mat. Inst. Steklova, 278, MAIK Nauka/Interperiodica, Moscow, 2012, 102–113; Proc. Steklov Inst. Math., 278 (2012), 94–105
Linking options:
https://www.mathnet.ru/eng/tm3405 https://www.mathnet.ru/eng/tm/v278/p102
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