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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Morse theory for codimension-one foliations


Authors: Steven C. Ferry and Arthur G. Wasserman
Journal: Trans. Amer. Math. Soc. 298 (1986), 227-240
MSC: Primary 57R30; Secondary 57R45, 58C27
MathSciNet review: 857441
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Abstract: It is shown that a smooth codimension-one foliation on a compact simply-connected manifold has a compact leaf if and only if every smooth real-valued function on the manifold has a cusp singularity.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0857441-5
PII: S 0002-9947(1986)0857441-5
Keywords: Codimension-one foliation, compact leaf, Morse theory, cusp singularity
Article copyright: © Copyright 1986 American Mathematical Society