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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2012, Volume 278, Pages 102–113 (Mi tm3405)  

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
Full-text PDF (232 kB) Citations (1)
References:
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
English version:
Proceedings of the Steklov Institute of Mathematics, 2012, Volume 278, Pages 94–105
DOI: https://doi.org/10.1134/S0081543812060107
Bibliographic databases:
Document Type: Article
UDC: 515.165+515.168.3+517.938.5
Language: Russian
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
Citation in format AMSBIB
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\by N.~I.~Zhukova
\paper Compact leaves of structurally stable foliations
\inbook Differential equations and dynamical systems
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2012
\vol 278
\pages 102--113
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\jour Proc. Steklov Inst. Math.
\yr 2012
\vol 278
\pages 94--105
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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