On the variations of the Betti numbers of regular levels of Morse flows
| Autor: | K. A. de Rezende, O. Manzoli Neto, Gioia M. Vago, Maria Alice Bertolim |
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| Rok vydání: | 2011 |
| Předmět: |
Lyapunov function
Betti number Handle decomposition Homology (mathematics) Betti's theorem Manifold TOPOLOGIA-GEOMETRIA Combinatorics symbols.namesake Ogasa invariant symbols Betti numbers Conley index theory Geometry and Topology Invariant (mathematics) Mathematics::Symplectic Geometry Conley index Mathematics |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| ISSN: | 0166-8641 |
| DOI: | 10.1016/j.topol.2011.01.021 |
| Popis: | We generalize results in Cruz and de Rezende (1999) [7] by completely describing how the Betti numbers of the boundary of an orientable manifold vary after attaching a handle, when the homology coefficients are in Z, Q, R or Z p Z with p prime. First we apply this result to the Conley index theory of Lyapunov graphs. Next we consider the Ogasa invariant associated with handle decompositions of manifolds. We make use of the above results in order to obtain upper bounds for the Ogasa invariant of product manifolds. |
| Databáze: | OpenAIRE |
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