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Doctoral Thesis
DOI
10.11606/T.55.2008.tde-08052008-135109
Document
Author
Full name
Grazielle Feliciani Barbosa
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2008
Supervisor
Committee
Saia, Marcelo José (President)
Atique, Roberta Godoi Wik
Birbrair, Lev
Garcia, Ronaldo Alves
Tomazella, João Nivaldo
Title in Portuguese
Topologia de singularidades e o estudo de seus invariantes
Keywords in Portuguese
Classificação de superfícies
Invariantes
Multiplicidade
Números de Milnor
Abstract in Portuguese
Algumas relações entre A-invariantes de germes de aplicações de coposto 1 equidimensionais f : 'C POT. n' , 0 'SETA' "C POT.n', 0 são descritas. O principal resultado estabelece que a soma alternada de números de Milnor dos fechos dos conjuntos Ai na fonte de f é igual a multiplicidade local de f menos n + 1. E existem fórmulas correspondentes para os s-tipos estáveis locais A('k IND.1' ,...'k IND.s'). As relações nos garantem condiçõoes para a A-finitude de f e para a A-trivialidade topológica de deformações de f. Também classificamos os germes de aplicações A-simples f : 'C POT.2', 0 'SETA' 'C POT.5', 0, para multiplicidades 1, 2 e 3
Title in English
Topology of singularities and the study of invariants
Keywords in English
Classification of surfaces
Invariants
Milnor numbers
Multiplicity
Abstract in English
Some new relations between A-invariants of equidimensional corank-1 map germs f :'C POT.n', 0 ' 'ARROW' 'C POT.n', 0 are described. The main local result states that the alternating sum ofthe Milnor numbers of the closures of the Ai sets in the source of f is equal to the local multiplicity of f minus n + 1. And there are corresponding formulas for the s-local stable types A('k IND.1' ,...,'k IND.s'). The realations provide simplified (or weaker) conditions for the A-finiteness of f and for the topological A-triviality of deformations of f. We also classify the A-simple germs f : 'C POT.2', 0 'ARROW' 'C POT.5', 0 for multiplicities 1, 2, and 3
 
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cinco.pdf (356.51 Kbytes)
Publishing Date
2008-05-08
 
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