Detectando fatores de variedade de codimensão um com propriedades de posição geral

• Autor(a) principal: Monteiro, Silvestre da Cruz
• Data de Publicação: 2010
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFSCAR
• Texto Completo: https://repositorio.ufscar.br/handle/ufscar/5866
• topic: Topologia algébrica; Topologia; Variedades topológicas; Variedades homológicas; Teoremas de extensão; Variedades generalizadas; Propriedades de posição geral; Generalized manifolds; Codimension one manifold factors, General Position; Properties; Extension theorems; Topology; CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA::TOPOLOGIA ALGEBRICA

This work is an approach to the famous "Product with a Line Problem". It investigates the class of topological spaces whose cartesian product with R is a topological manifold. Such spaces are called "Codimension One Manifold Factors". Based mainly on [5, 7, 14, 15, 24], we introduce the concept of generalized manifolds, which are separable ANR spaces with same local homological behavior that the topological manifolds, we define DAP, DADP, DDP, DHP, DCP general position properties and, through these concepts and a machinery topological-algebraic, we have got answers to the motivator problem. Even about the strategic importance of the DHP general position property, we studied a criterion to detect it into the generalized manifolds category, namely, the P2MP.