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JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova // Archive

Trudy Mat. Inst. Steklova, 2012 Volume 278, Pages 102–113 (Mi tm3405)

This article is cited 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.

UDC: 515.165+515.168.3+517.938.5

Received in March 2011


 English version:
Proceedings of the Steklov Institute of Mathematics, 2012, 278, 94–105

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