Stability of foliations
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- by Harold I. Levine and Michael Shub PDF
- Trans. Amer. Math. Soc. 184 (1973), 419-437 Request permission
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 ${\prod _1}(X)$ in the group of germs at 0 of 0-fixed self-diffeomorphisms of ${{\text {R}}^k}$ 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.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 184 (1973), 419-437
- MSC: Primary 58A30; Secondary 57D30
- DOI: https://doi.org/10.1090/S0002-9947-1973-0331417-X
- MathSciNet review: 0331417