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Maximal Poincaré polynomials and minimal Morse functions


Authors: V. Benci and K. A. de Rezende
Journal: Proc. Amer. Math. Soc. 129 (2001), 3511-3518
MSC (2000): Primary 37D15, 37C10; Secondary 54H20, 37B30
Published electronically: July 17, 2001
MathSciNet review: 1860482
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Abstract:

In this paper we introduce the maximum Poincaré polynomial $P^{\ast} (M)$ of a compact manifold $M$, 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 $M$.


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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: https://doi.org/10.1090/S0002-9939-01-06290-6
Received by editor(s): December 7, 1999
Published electronically: July 17, 2001
Additional Notes: This research was supported by the Conselho Nacional de Desenvolvimento Científico e Tecnológico under Grant 300072/90.2.
Communicated by: Michael Handel
Article copyright: © Copyright 2001 American Mathematical Society