An algebraic-topological approach to dynamical systems and symplectic topology
Spectral sequences for Morse-Bott and Morse-Novikov flows study
| Full text | |
| Author(s): |
Bertolim, Maria A.
[1]
;
Lima, Dahisy V. S.
[2]
;
Mello, Margarida P.
[2]
;
de Rezende, Ketty A.
[2]
;
da Silveira, Mariana R.
[3]
Total Authors: 5
|
| Affiliation: | [1] SRH Leonardo da Vinci Gymnasium, Spitzerfeld 25, D-69151 Neckargemund - Germany
[2] Univ Estadual Campinas, IMECC, BR-13083859 Campinas, SP - Brazil
[3] Univ Fed ABC, CMCC, BR-09210580 Santo Andre, SP - Brazil
Total Affiliations: 3
|
| Document type: | Journal article |
| Source: | EUROPEAN JOURNAL OF MATHEMATICS; v. 3, n. 2, p. 387-428, JUN 2017. |
| Web of Science Citations: | 0 |
| Abstract | |
We study algorithms that give rise to a global Smale's Cancellation Theorem for dimensions n >= 6. The Spectral Sequence Sweeping Algorithm (SSSA) and the Row Cancellation Algorithm (RCA) for a filtered Morse chain complex on a manifold M-n are presented. Our main theorems, which make use of these algorithms with a connection matrix as an input, establish a correspondence between algebraic cancellations in a spectral sequence and dynamical cancellations of the gradient flow on M-n for dimensions n >= 6. (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: | 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 |