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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On foliations with Morse singularities


Authors: César Camacho and Bruno Scardua
Journal: Proc. Amer. Math. Soc. 136 (2008), 4065-4073
MSC (2000): Primary 57R30, 58E05; Secondary 57R70, 57R45
Published electronically: June 9, 2008
MathSciNet review: 2425748
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Abstract | References | Similar Articles | Additional Information

Abstract: We study codimension one smooth foliations with Morse type singularities on closed manifolds. We obtain a description of the manifold if there are more centers than saddles. This result relies on and extends previous results of Reeb for foliations having only centers, results of Wagneur for foliations with Morse singularities and results of Eells and Kuiper for manifolds admitting Morse functions with three singularities.


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Additional Information

César Camacho
Affiliation: IMPA-Estrada D. Castorina, 110, Jardim Botânico, Rio de Janeiro - RJ, 22460-320 Brazil
Email: camacho@impa.br

Bruno Scardua
Affiliation: Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, Rio de Janeiro-RJ, 21945-970 Brazil
Email: scardua@impa.br

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09371-4
PII: S 0002-9939(08)09371-4
Keywords: Foliation, Morse singularity, holonomy.
Received by editor(s): September 11, 2007
Received by editor(s) in revised form: October 4, 2007
Published electronically: June 9, 2008
Additional Notes: The second author is supported by the ICTP Associateship program.
Communicated by: Jane M. Hawkins
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.