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Master's Dissertation
DOI
10.11606/D.55.2017.tde-27072017-103944
Document
Author
Full name
Juan Carlos Nuñez Maldonado
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2017
Supervisor
Committee
Santos, Raimundo Nonato Araújo dos (President)
Costa, João Carlos Ferreira
Ruas, Maria Aparecida Soares
Santos, Edivaldo Lopes dos
Title in Portuguese
Conectividade  de  variedades  semi-algébricas
Keywords in Portuguese
Conexidade de hipersuperficies genérica
Estrutura de conjuntos semi-algébricos
Ponto focal e teorema de Lefschetz
Teorema da fibração local e global
Topologia das fibras e do link
Abstract in Portuguese
Neste projeto apresentamos os teoremas de estrutura, decomposição celular, e o teorema da existência da triangulação para conjuntos semi-algébricos compactos. Como aplicações destes teoremas mostramos o lema de seleção da curva local e global. Além disso, apresentamos uma breve descrição da topologia da fibra de Milnor local e global, bem como alguns resultados sobre o grau de conexidade da fibra genérica global de uma função polinomial complexa, que mostram a íntima relação entre o grau de conexidade com a dimensão do conjunto singular.
Title in English
Connectivity of semialgebraic sets
Keywords in English
Focal point and Lefschetz theorem
Milnor fibration local and global
On the connectivity of generic hypersurfaces
Structure of Semi-algebraic sets
Topology of the fibers and link
Abstract in English
In this project we present some structure theorems, cell decomposition, and the theorem on the existence of triangulation for compact semi-algebraic sets. As applications we prove the curve selection lemma in the local and global cases. Moreover, we present a brief description about the topology of local and global Milnor´s fibers, as well as, some results about the connectivity degree of the generic fibers of a complex polynomial function, that show the close relation between the connectivity degree and the dimension of the singular locus.
 
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Publishing Date
2017-07-27
 
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