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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 | References | Similar Articles | Additional Information


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 $M$.

References [Enhancements On Off] (What's this?)

  • [Co] Octav Cornea, The genus and the fundamental group of high-dimensional manifolds, Stud. Cerc. Mat. 41 (1989), no. 3, 169–178. MR 1010874
  • [dR] K. A. de Rezende, Gradient-like flows on 3-manifolds, Ergodic Theory Dynam. Systems 13 (1993), no. 3, 557–580. MR 1245829, 10.1017/S0143385700007525
  • [Fr] John M. Franks, Homology and dynamical systems, CBMS Regional Conference Series in Mathematics, vol. 49, Published for the Conference Board of the Mathematical Sciences, Washington, D.C.; by the American Mathematical Society, Providence, R. I., 1982. MR 669378
  • [Sm] Stephen Smale, Generalized Poincaré’s conjecture in dimensions greater than four, Ann. of Math. (2) 74 (1961), 391–406. MR 0137124

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Additional Information

V. Benci
Affiliation: Departament of Applied Mathematics, University of Pisa, Pisa, Italy

K. A. de Rezende
Affiliation: Departamento de Matemática, Universidade Estadual de Campinas, 13083-970 Campinas, São Paulo, Brazil

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