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On foliations with Morse singularities
Author(s):
César
Camacho;
Bruno
Scardua
Journal:
Proc. Amer. Math. Soc.
136
(2008),
4065-4073.
MSC (2000):
Primary 57R30, 58E05;
Secondary 57R70, 57R45
Posted:
June 9, 2008
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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.
References:
-
- 1.
- C. Camacho, A. Lins Neto: Geometric Theory of Foliations, Birkhäuser Boston, 1985. MR 824240 (87a:57029)
- 2.
- C. Camacho, B. Scárdua: On codimension one foliations with Morse singularities on three-manifolds, Topology and Its Applications, Volume 154, Issue 6, 15 March 2007, pp. 1032-1040. MR 2298620
- 3.
- J. Eells, N. Kuiper: Manifolds which are like projective planes, Pub. I.H.E.S., 14 (1962), pp. 5-46. MR 0145544 (26:3075)
- 4.
- J. Eells, N. Kuiper: Closed manifolds which admit nondegenerate functions with three critical points, Indag. Math. 23 (1961), pp. 411-417. MR 0139176 (25:2612)
- 5.
- C. Godbillon: Feuilletages. Études géométriques. With a preface by G. Reeb. Progress in Mathematics, 98. Birkhäuser-Verlag, Basel, 1991. MR 1120547 (93i:57038)
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- J. Milnor: Morse Theory, Annals of Mathematics Studies, Number 51, Princeton Univ. Press, Princeton, N.J., 1963. MR 0163331 (29:634)
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- 8.
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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:
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
Posted:
June 9, 2008
Additional Notes:
The second author is supported by the ICTP Associateship program.
Communicated by:
Jane M. Hawkins
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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