On handle theory for Morse-Bott critical manifolds

Autor(es)

Lima, D. V. S. ^[1] ; Manzoli Neto, O. ^[2] ; de Rezende, K. A. ^[3]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: Geometriae Dedicata; v. 202, n. 1, p. 265-309, OCT 2019.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 12/18780-0 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos
• Beneficiário: Marco Antônio Teixeira
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 16/24707-4 - Topologia algébrica, geométrica e diferencial
• Beneficiário: Daciberg Lima Gonçalves
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• 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