Spectral sequences for Morse-Bott and Morse-Novikov flows study
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| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Fed ABC, CMCC, Santo Andre, SP - Brazil
[2] Univ Sao Paulo, ICMC, Sao Carlos, SP - Brazil
[3] Univ Estadual Campinas, IMECC, Campinas, SP - Brazil
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | Geometriae Dedicata; v. 202, n. 1, p. 265-309, OCT 2019. |
| Web of Science Citations: | 0 |
| Abstract | |
In this article, we use Conley Index Theory to set up a framework to associate topological-dynamical invariants to a Morse-Bott flow in a neighborhood of a critical manifold. Isolating blocks N for a critical manifold S are characterized in terms of conditions on the ranks of its homology Conley index. The necessity of these conditions follows from the generalized Morse-Bott inequalities for isolating blocks. Morse-Bott semi-graphs turn out to be a useful combinatorial device to record these topological conditions. One goal is to verify that these conditions when imposed on an n-abstract Morse-Bott semi-graph are sufficient for its realization. This is attained by introducing Morse-Bott handle surgeries in order to construct isolating blocks for critical manifolds in dimensions 2 and 3, and for a large class in higher dimensions. Stronger results are obtained in dimensions 2 and 3 where necessary and sufficient conditions for a Morse-Bott graph to be associated to a Morse-Bott flow on some manifold M are determined. (AU) | |
| FAPESP's process: | 12/18780-0 - Geometry of control systems, dynamical and stochastics systems |
| Grantee: | Marco Antônio Teixeira |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 16/24707-4 - Algebraic, geometric and differential topology |
| Grantee: | Daciberg Lima Gonçalves |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 14/11943-6 - Spectral sequences for Morse-Bott and Morse-Novikov flows study |
| Grantee: | Dahisy Valadão de Souza Lima |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |