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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Maximal Poincaré polynomials and minimal Morse functions
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by V. Benci and K. A. de Rezende PDF
Proc. Amer. Math. Soc. 129 (2001), 3511-3518 Request permission

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 $M$.
References
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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
  • 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
  • © Copyright 2001 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 129 (2001), 3511-3518
  • MSC (2000): Primary 37D15, 37C10; Secondary 54H20, 37B30
  • DOI: https://doi.org/10.1090/S0002-9939-01-06290-6
  • MathSciNet review: 1860482