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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.)

HOMOTOPICAL CANCELLATION THEORY FOR GUTIERREZ-SOTOMAYOR SINGULAR FLOWS

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Author(s):
Lima, D. V. S. [1] ; Raminelli, S. A. [2] ; de Rezende, K. A. [2]
Total Authors: 3
Affiliation:
[1] Univ Fed ABC, CMCC, Santo Andre, SP - Brazil
[2] Univ Estadual Campinas, IMECC, Campinas, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: JOURNAL OF SINGULARITIES; v. 23, p. 33-91, 2021.
Web of Science Citations: 0
Abstract

In this article, we present a dynamical homotopical cancellation theory for Gutierrez-Sotomayor singular flows phi, GS-flows, on singular surfaces M. This theory generalizes the classical theory of Morse complexes of smooth dynamical systems together with the corresponding cancellation theory for non-degenerate singularities. This is accomplished by defining a GS-chain complex for (M, phi) and computing its spectral sequence (E-r, d(r)). As r increases, algebraic cancellations occur, causing modules in E-r to become trivial. The main theorems herein relate these algebraic cancellations within the spectral sequence to a family [M-r, phi(r)] of GS-flows phi(r) on singular surfaces M-r, all of which have the same homotopy type as M. The surprising element in these results is that the dynamical homotopical cancellation of GS-singularities of the flows phi(r) are in consonance with the algebraic cancellation of the modules in E-r of its associated spectral sequence. Also, the convergence of the spectral sequence corresponds to a GS-flow phi((r) over bar) on M-(r) over bar, for some (r) over bar, with the property that phi((r) over bar) admits no further dynamical homotopical cancellation of GS-singularities. (AU)

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
FAPESP's process: 18/13481-0 - Geometry of control, dynamical and stochastic systems
Grantee:Marco Antônio Teixeira
Support type: Research Projects - Thematic Grants
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: 16/24707-4 - Algebraic, geometric and differential topology
Grantee:Daciberg Lima Gonçalves
Support type: Research Projects - Thematic Grants