|
|||||
|
|
Poincaré-Hopf inequalities |
|
| Authors: | M A Bertolim M P Mello K A de Rezende |
| Institution: | Department of Mathematics, Institute of Mathematics, Statistics and Scientific Computation, Unicamp, Campinas, São Paulo, Brazil ; Department of Applied Mathematics, Institute of Mathematics, Statistics and Scientific Computation, Unicamp, Campinas, São Paulo, Brazil ; Department of Mathematics, Institute of Mathematics, Statistics and Scientific Computation, Unicamp, Campinas, São Paulo, Brazil |
| 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. |
| Keywords: | Conley index Morse inequalities Morse polytope integral polytope network-flow theory |
| 点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息 | |
| 点击此处可从《Transactions of the American Mathematical Society》下载免费的PDF全文 | |