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Remarks on structurally stable proper foliations

Published online by Cambridge University Press:  24 October 2008

Marco Brunella
Marco Brunella
Affiliation:
Dipartimento di Matematica, Piazza di Porta S. Donato 5, I-40127 Bologna, Italy
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Extract

Let M be a closed manifold of dimension 3 and let Fol(M) be the space of codimension one C∞-foliations on M. A foliation ∈ Fol(M) is said to be Cr- structurally stable if there exists a neighbourhood V of in Fol(M) in the (Epstein) Cr-topology such that every foliation is topologically conjugate to , through a homeomorphism near to the identity. Some background on the problem of structural stability of foliations can be found in [8]. In this paper we shall be concerned with proper foliations, i.e. foliations all of whose leaves are proper.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 115 , Issue 1 , January 1994 , pp. 111 - 120
Copyright
Copyright © Cambridge Philosophical Society 1994

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References

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