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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

CANCELLATIONS FOR CIRCLE-VALUED MORSE FUNCTIONS VIA SPECTRAL SEQUENCES

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Author(s):
Lima, Dahisy V. de S. [1] ; Manzoli Neto, Oziride [2] ; de Rezende, Ketty A. [1] ; da Silveira, Mariana R. [3]
Total Authors: 4
Affiliation:
[1] Univ Estadual Campinas, IMECC, Campinas, SP - Brazil
[2] Univ Sao Paulo, ICMC, Sao Carlos, SP - Brazil
[3] Univ Fed ABC, CMCC, Santo Andre, SP - Brazil
Total Affiliations: 3
Document type: Journal article
Source: TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS; v. 51, n. 1, p. 259-311, MAR 2018.
Web of Science Citations: 0
Abstract

A spectral sequence analysis of a filtered Novikov complex (N-{*}(f), Delta) over Z ((t)) is developed with the goal of obtaining results relating the algebraic and dynamical settings. Specifically, the unfolding of a spectral sequence of (N-{*}(f), Delta) and the cancellation of its modules is associated to a one parameter family of circle-valued Morse functions on a surface and the dynamical cancellations of its critical points. The data of a spectral sequence computed for (N-{*}(f), Delta) is encoded in a family of matrices Delta(r) produced by the Spectral Sequence Sweeping Algorithm (SSSA), which has as its initial input the differential Delta. As one ``turns the pages{''} of the spectral sequence, differentials which are isomorphisms produce cancellation of pairs of modules. Corresponding to these cancellations, a family of circle-valued Morse functions f(r) is obtained by successively removing the corresponding pairs of critical points of f. We also keep track of all dynamical information on the birth and death of connecting orbits between consecutive critical points, as well as periodic orbits that arise within a family of negative gradient flows associated to f(r). (AU)

FAPESP's process: 15/10930-0 - Symplectic dynamics and spectral sequences
Grantee:Dahisy Valadão de Souza Lima
Support type: Scholarships abroad - Research Internship - Post-doctor
FAPESP's process: 12/18780-0 - Geometry of control systems, dynamical and stochastics systems
Grantee:Marco Antônio Teixeira
Support type: 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 type: Scholarships in Brazil - Post-Doctorate