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Maximal Poincaré polynomials and minimal Morse functions
Author(s):
V.
Benci;
K.
A.
de Rezende
Journal:
Proc. Amer. Math. Soc.
129
(2001),
3511-3518.
MSC (2000):
Primary 37D15, 37C10;
Secondary 54H20, 37B30
Posted:
July 17, 2001
MathSciNet review:
1860482
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Abstract:
In this paper we introduce the maximum Poincaré polynomial of a compact manifold , and prove its uniqueness. We show that its coefficients are topological invariants of the manifolds which, in some cases, correspond to known ones. We also investigate its realizability via a Morse function on .
References:
-
- [Co]
- O. Cornea, The genus and the fundamental group of high-dimensional manifolds, Stud. Cerc. Mat. 41, n.3 (1989) pp.169-178. MR 90h:57022
- [dR]
- K. de Rezende, Gradient-like flows on 3-manifolds, Ergod. Th. and Dynam. Sys. 13 (1993) pp.557-580. MR 94j:58146
- [Fr]
- J. M. Franks, Homology and Dynamical Systems, CBMS 49 (1982). MR 84f:58067
- [Sm]
- S. Smale, Generalized Poincaré's conjecture in dimensions greater than four, Annals of Mathematics 74 (1961) pp.391-406. MR 25:580
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Additional Information:
V.
Benci
Affiliation:
Departament of Applied Mathematics, University of Pisa, Pisa, Italy
Email:
benci@dm.unipi.it
K.
A.
de Rezende
Affiliation:
Departamento de Matemática, Universidade Estadual de Campinas, 13083-970 Campinas, São Paulo, Brazil
Email:
ketty@ime.unicamp.br
DOI:
10.1090/S0002-9939-01-06290-6
PII:
S 0002-9939(01)06290-6
Received by editor(s):
December 7, 1999
Posted:
July 17, 2001
Additional Notes:
This research was supported by the Conselho Nacional de Desenvolvimento Cientí{}fico e Tecnológico under Grant 300072/90.2.
Communicated by:
Michael Handel
Copyright of article:
Copyright
2001,
American Mathematical Society
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