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Mémoire de Maîtrise
DOI
https://doi.org/10.11606/D.55.2010.tde-22062010-091958
Document
Auteur
Nom complet
Norbil Leodan Cordova Neyra
Adresse Mail
Unité de l'USP
Domain de Connaissance
Date de Soutenance
Editeur
São Carlos, 2010
Directeur
Jury
Mattos, Denise de (Président)
Goncalves, Daciberg Lima
Pergher, Pedro Luiz Queiroz
 
Titre en portugais
Teorida de G-índice e grau de aplicações G-equivariantes
Mots-clés en portugais
Aplicações G-equivariantes
Cohomologia de Cech
Espaços classificantes
G-espaços
G-índice
Grau
Resumé en portugais
Antes da publicação do trabalho An ideal-valued cohomological index theory with applications to Borsuk-Ulam and Bourgin-Yang theorems"de Fadell e Husseini [20], haviam sido apenas considerados índices numéricos de G-espaços, nos casos G ='Z IND. 2' e G um grupo finito. No entanto, tais índices numéricos são obviamente insuficientes no caso de grupos mais complexos, como por exemplo a 1-esfera 'S POT. 1'. Neste contexto, Fadell e Husseini introduziram o chamado Indice cohomológico de valor ideal: a cada G-espaço X paracompacto, eles associaram um ideal 'Ind POT. G' (X;K) do anel de cohomología H*(BG;K), onde a cohomologia de Cech H* é considerada com coeficientes em um corpo K e BG é o espaço classificante do grupo G. Além disso, Fadell e Husseini associaram a este ideal o Índice cohomológico de valor numérico, o qual é definido como sendo a dimensão do K-espaço vetorial obtido do quociente entre o anel H*(BG;K) e o ideal 'Ind POT. G' (X;K). O objetivo principal deste trabalho é apresentar um estudo detalhado deste índice e utilizá-lo no estudo dos resultados sobre grau de aplicações G-equivariantes provados por Hara em "The degree of equivariant maps"[24]
 
Titre en anglais
G-index theory and degree of G-equivariant maps
Mots-clés en anglais
Cech cohomology
Classifying spaces
Degree
G-equivariant maps
G-index
G-spaces
Resumé en anglais
Before the appearance of the paper An ideal-valued cohomological index theory with applications to Borsuk-Ulam and Bourgin-Yang theorems"of Fadell and Husseini [20], had been considered numerical indices of G-spaces, when G = 'Z IND. 2' and when G is a finite group. However, such numerical indices are obviously insufficient in the case of groups more complexes, for example, G ='S POT 1'. In this context Fadell andHusseini, introduced the called valued-ideal cohomological index: to every paracompact G-space X they associated an ideal 'Ind POT. G' (X,K) of the cohomology ring H*(BG;K), where the Cech cohomology H* is considered with coefficients in a field K and BG is the classifying space of the group G. Moreover, they associated to this ideal the numerical valued cohomological index, that is, the dimension of K-vector space obtained by the quotient between the ring H*(BG;K) and the ideal 'Ind POT. G' (X,K). The main objective of this work is to present a detailed study of this index and use such index on the study of results on degree of equivariant maps proved by Hara in his paper The degree of equivariant maps"[24]
 
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Date de Publication
2010-06-22
 
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