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Doctoral Thesis
DOI
10.11606/T.55.2018.tde-06072018-115031
Document
Author
Full name
Maico Felipe Silva Ribeiro
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2018
Supervisor
Committee
Santos, Raimundo Nonato Araújo dos (President)
Costa, João Carlos Ferreira
Ruas, Maria Aparecida Soares
Scardua, Bruno Cesar Azevedo
Title in English
Singular Milnor Fibrations
Keywords in English
Local fibration structures
Milnor sphere fibration
Milnor tube fibration
Mixed singularities
Real and complex singularities
Regularity conditions
Stratification theory
Stratified fibration structures
Abstract in English
In this work we present the most recent developments in the direction of local fibrations structures of analytic singularities. Using techniques and tools from stratification theory we prove structural theorems in the stratified sense, which will be called singular Milnor tube fibration and Milnor-Hamm sphere fibration. In addition, we present algorithms with the purpose of creating a large number of examples in this new setting and compare our results obtained with the current ones found in the literature. Our results generalize all previous result in both cases: in the classical and in the stratified ones.
Title in Portuguese
Fibrações de Milnor singulares
Keywords in Portuguese
Condições de regularidade
Estruturas de fibração estratificadas
Estruturas de fibração local
Fibrações de Milnor sobre esferas
Fibrações de Milnor sobre tubo
Singularidades mistas
Singularidades reais e complexas
Teoria de stratificação
Abstract in Portuguese
Neste trabalho apresentamos os mais recentes desenvolvimentos na direção de estruturas de fibrações locais de singularidades analíticas. Usando técnicas e ferramentas da teoria de estratificação, provamos alguns teoremas estruturais no sentido estratificado, os quais serão chamados fibração singular de Milnor sobre o tubo e fibração de Milnor-Hamm sobre a esfera. Além disso, apresentamos algoritmos com o intuito de criar uma ampla variedade de exemplos e comparamos nossos resultados com os atuais encontrados na literatura. Nossos resultados generalizam todos os previamente existentes tanto no caso clássico, quanto no sentido estratificado.
 
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Publishing Date
2018-07-06
 
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