Poincaré-Hopf inequalities
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- by M. A. Bertolim, M. P. Mello and K. A. de Rezende PDF
- Trans. Amer. Math. Soc. 357 (2005), 4091-4129 Request permission
Abstract:
In this article the main theorem establishes the necessity and sufficiency of the Poincaré-Hopf inequalities in order for the Morse inequalities to hold. The convex hull of the collection of all Betti number vectors which satisfy the Morse inequalities for a pre-assigned index data determines a Morse polytope defined on the nonnegative orthant. Using results from network flow theory, a scheme is provided for constructing all possible Betti number vectors which satisfy the Morse inequalities for a pre-assigned index data. Geometrical properties of this polytope are described.References
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Additional Information
- M. A. Bertolim
- Affiliation: Department of Mathematics, Institute of Mathematics, Statistics and Scientific Computation, Unicamp, Campinas, São Paulo, Brazil
- Email: bertolim@ime.unicamp.br
- M. P. Mello
- Affiliation: Department of Applied Mathematics, Institute of Mathematics, Statistics and Scientific Computation, Unicamp, Campinas, São Paulo, Brazil
- Email: margarid@ime.unicamp.br
- K. A. de Rezende
- Affiliation: Department of Mathematics, Institute of Mathematics, Statistics and Scientific Computation, Unicamp, Campinas, São Paulo, Brazil
- Email: ketty@ime.unicamp.br
- Received by editor(s): February 6, 2003
- Received by editor(s) in revised form: December 2, 2003
- Published electronically: October 28, 2004
- Additional Notes: The first author was supported by FAPESP under grant 02/08400-3
The second author was supported by CNPq-PRONEX Optimization and by FAPESP under grant 01/04597-4
The third author was partially supported by FAPESP under grants 00/05385-8 and 02/102462, and by CNPq under grant 300072 - © Copyright 2004 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 357 (2005), 4091-4129
- MSC (2000): Primary 37B30, 37B35, 37B25; Secondary 54H20
- DOI: https://doi.org/10.1090/S0002-9947-04-03641-4
- MathSciNet review: 2159701