Master's Dissertation
DOI
https://doi.org/10.11606/D.55.2010.tde-22062010-091958
Document
Author
Full name
Norbil Leodan Cordova Neyra
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2010
Supervisor
Committee
Mattos, Denise de (President)
Goncalves, Daciberg Lima
Pergher, Pedro Luiz Queiroz
Title in Portuguese
Teorida de G-índice e grau de aplicações G-equivariantes
Keywords in Portuguese
Aplicações G-equivariantes
Cohomologia de Cech
Espaços classificantes
G-espaços
G-índice
Grau
Abstract in Portuguese
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]
Title in English
G-index theory and degree of G-equivariant maps
Keywords in English
Cech cohomology
Classifying spaces
Degree
G-equivariant maps
G-index
G-spaces
Abstract in English
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]
WARNING - Viewing this document is conditioned on your acceptance of the following terms of use:
This document is only for private use for research and teaching activities. Reproduction for commercial use is forbidden. This rights cover the whole data about this document as well as its contents. Any uses or copies of this document in whole or in part must include the author's name.
norbil.pdf (563.66 Kbytes)
Publishing Date
2010-06-22