Artículos de revistas
Classical Morse Theory Revisited – I Backward λ-lemma And Homotopy Type
Registro en:
Topological Methods In Nonlinear Analysis. Juliusz Schauder Center For Nonlinear Studies, v. 47, n. 2, p. 641 - 646, 2016.
1230-3429
10.12775/TMNA.2016.020
2-s2.0-84978708727
Autor
Weber J.
Institución
Resumen
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) We introduce two tools, dynamical thickening and flow selectors, to overcome the infamous discontinuity of the gradient flow endpoint map near non-degenerate critical points. More precisely, we interpret the stable fibrations of certain Conley pairs (N;L), established in [2], as a dynamical thickening of the stable manifold. As a first application and to illustrate effciency of the concept we reprove a fundamental theorem of classical Morse theory, Milnor's homotopical cell attachment theorem [1]. Dynamical thickening leads to a conceptually simple and short proof. © 2016 Juliusz Schauder Centre for Nonlinear Studies. 47 2 641 646 CNPq, Conselho Nacional de Desenvolvimento Científico e Tecnológico 1135/2013, FAEPEX, Fundo de Apoio ao Ensino, à Pesquisa e Extensão 2013/20912-4, FAPESP, Fundação de Amparo à Pesquisa do Estado de São Paulo Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)