Pontos fixos e os contra-exemplos de Jiang

• Autor(a) principal: Souza, Taciana Oliveira
• Data de Publicação: 2009
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFSCAR
• Texto Completo: https://repositorio.ufscar.br/handle/ufscar/5860
• topic: Topologia algébrica; Pontos fixos; Grupo de tranças; CIENCIAS EXATAS E DA TERRA::MATEMATICA

The aim of this work is construct the example, presented by Boju Jiang, of a self - map on a manifold with non - realizable Nielsen number. Firstly we will need to present the fixed point theory and some results about covering spaces, we do that in chapter 1. The chapter 2 is dedicated to obtain one presentation of the braid group of the Pants, that is the manifold used in Jiang´s example. This presentation is a very important tool and it will be used in the main results of this work. In the chapter 3 we construct the self - map. The aim of chapter 4 is to proof the following theorem: Let M be a compact, connected surface with negative Euler caracteristic. Then there exist a self - map on M such that all maps in its homotopy class have at least one fixed point, but its Nielsen number is zero . This result shows that even for the manifold without bondary it is possible to find self - maps with non - realizable Nielsen number. In chapter 3 e 4 we use Braid Group to construct such counter - examples, in the chapter 5 (the last one) we related some equation in braid group with the number of fixed points of a self - map on a compact connected surface.