HOMOTOPICAL CANCELLATION THEORY FOR GUTIERREZ-SOTOMAYOR SINGULAR FLOWS

Autor(es)

Lima, D. V. S. ^[1] ; Raminelli, S. A. ^[2] ; de Rezende, K. A. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Fed ABC, CMCC, Santo Andre, SP - Brazil

^[2] Univ Estadual Campinas, IMECC, Campinas, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF SINGULARITIES; v. 23, p. 33-91, 2021.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 14/11943-6 - Sequências espectrais no estudo de fluxos de Morse-Bott e Morse-Novikov
• Beneficiário: Dahisy Valadão de Souza Lima
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 18/13481-0 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos
• Beneficiário: Marco Antônio Teixeira
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 15/10930-0 - Dinâmica simplética e sequências espectrais
• Beneficiário: Dahisy Valadão de Souza Lima
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Pós-Doutorado
• Processo FAPESP: 16/24707-4 - Topologia algébrica, geométrica e diferencial
• Beneficiário: Daciberg Lima Gonçalves
• Modalidade de apoio: Auxílio à Pesquisa - Temático