dc.contributor | Töben, Dirk | |
dc.contributor | http://lattes.cnpq.br/0022267686144981 | |
dc.contributor | http://lattes.cnpq.br/6854004362377096 | |
dc.creator | Ferreira, Junio Cesar | |
dc.date.accessioned | 2022-03-08T10:27:36Z | |
dc.date.accessioned | 2022-10-10T21:39:05Z | |
dc.date.available | 2022-03-08T10:27:36Z | |
dc.date.available | 2022-10-10T21:39:05Z | |
dc.date.created | 2022-03-08T10:27:36Z | |
dc.date.issued | 2022-02-14 | |
dc.identifier | FERREIRA, Junio Cesar. Categoria de Lusternik-Schnirelmann e aplicações. 2022. Dissertação (Mestrado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2022. Disponível em: https://repositorio.ufscar.br/handle/ufscar/15674. | |
dc.identifier | https://repositorio.ufscar.br/handle/ufscar/15674 | |
dc.identifier.uri | http://repositorioslatinoamericanos.uchile.cl/handle/2250/4045751 | |
dc.description.abstract | The Lusternik-Schnirelmann category associates a positive integer to each topological space. This number is an important invariant in algebraic topology, critical point theory and symplectic geometry. In this dissertation we present the theory of Lusternik-Schnirelmann category, compute the category of several topological spaces and provide some reformulations of the category. In addition, we show two applications of Lusternik-Schnirelmann category to other areas of mathematics. The first one is a geometric application proving that a convex body in Euclidean space of dimension n admits at least n binormal chords. The second application relates the category to topological complexity in the motion planning problem. | |
dc.language | por | |
dc.publisher | Universidade Federal de São Carlos | |
dc.publisher | UFSCar | |
dc.publisher | Programa de Pós-Graduação em Matemática - PPGM | |
dc.publisher | Câmpus São Carlos | |
dc.rights | http://creativecommons.org/licenses/by-nc-nd/3.0/br/ | |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Brazil | |
dc.subject | Categoria de Lusternik-Schnirelmann | |
dc.subject | Topologia algébrica | |
dc.subject | Pontos críticos | |
dc.subject | Cordas binormais | |
dc.subject | Corpos convexos | |
dc.subject | Complexidade topológica | |
dc.subject | Lusternik-Schnirelmann category | |
dc.subject | Algebraic topology | |
dc.subject | Critical points | |
dc.subject | Cup length | |
dc.subject | Double normal chords | |
dc.subject | Convex bodies | |
dc.subject | Topological complexity | |
dc.title | Categoria de Lusternik-Schnirelmann e aplicações | |
dc.type | Tesis | |