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Transactions of the American Mathematical Society
Article . 1973 . Peer-reviewed
Data sources: Crossref
Transactions of the American Mathematical Society
Article . 1973 . Peer-reviewed
Data sources: Crossref
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Stability of Foliations

Stability of foliations
Authors: Michael Shub; Harold I. Levine;

Stability of Foliations

Abstract

Let X be a compact manifold and let k be an integer. It is shown that the set of homeomorphism conjugacy classes of germs at X of foliations of codimension k and the set of homeomorphism conjugacy classes of (holonomy) representations of ∏ 1 ( X ) {\prod _1}(X) in the group of germs at 0 of 0-fixed self-diffeomorphisms of R k {{\text {R}}^k} are homeomorphic when given appropriate topologies. Stable foliation germs and stable holonomy representations correspond under this homeomorphism. It is shown that there are no stable foliation germs at a toral leaf if the dimension of the torus is greater than one.

Keywords

Foliations in differential topology; geometric theory

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
5
Average
Top 10%
Average
bronze
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