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Master's Dissertation
DOI
https://doi.org/10.11606/D.55.2018.tde-14032018-091102
Document
Author
Full name
Claudemir Aniz
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1998
Supervisor
Committee
Manzoli Neto, Oziride (President)
Borsari, Lucilia Daruiz
Goncalves, Daciberg Lima
Title in Portuguese
O Número de Nielsen Relativo
Keywords in Portuguese
Não disponível
Abstract in Portuguese
O objetivo deste trabalho é introduzir o número de Nielsen relativo N(f; X, A), para aplicações f : (X, A) → (X, A) entre pares de espaços, com propriedades semelhantes aos do número de Nielsen, como invariância homotópica e invariância por tipo de homotopia. De N(f; X, A) ≥ N(f) = N (f; X, 0), o número de Nielsen relativo é no caso A ≠ 0 um limitante inferior melhor do que N(f)) para o número mínimo μ(f; X, A) de pontos fixos na classe de homotopia de f, onde as homotopias são aplicações da forma H: (X x I, A x I) → (X, A). Condições para um par (X, A) de poliedros finitos são dadas para assegurar que o número de Nielsen relativo é de fato o melhor limitante inferior, isto e, N(f; X, A) = μ(f; X, A).
Title in English
Not available
Keywords in English
Not available
Abstract in English
The purpose of this work is to introduce the relative Nielsen number N(f; X, A) for maps of pairs of spaces f : (X, A) → (X, A), with similar properties to the usual Nielsen number as homotopy invariance and homotopy type invariance. From N(f;; X, A) ≥ N(f) = N(f;; X, 0), the relative Nielsen number is in the case A ≠ 0 a better lower bound than N(f) for the minimum number μ(f ; X, A) of fixed points in the homotopy class of f, here homotopy means maps of pairs of the form H : (X x I, A x I) → (X, A). In the case (X, A) is a fmite polyhedral pair, conditions are given to guarantee that the relative Nielsen number is in fact the best lower bound, that is, N(f ; X, A) = μ( f ; X, A).
 
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ClaudemirAniz.pdf (806.11 Kbytes)
Publishing Date
2018-03-14
 
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