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Dimension of Virtually Cyclic Classifying Spaces for Certain Geometric GroupsJoecken, Kyle 25 September 2013 (has links)
No description available.
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On the Chow ring of the classifying space BSO (2n, C) /Field, Rebecca. January 2000 (has links)
Thesis (Ph. D.)--University of Chicago, Dept. of Mathematics, August 2000. / Includes bibliographical references. Also available on the Internet.
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Teorida de G-índice e grau de aplicações G-equivariantes / G-index theory and degree of G-equivariant mapsNeyra, Norbil Leodan Cordova 07 May 2010 (has links)
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] / 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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Teorida de G-índice e grau de aplicações G-equivariantes / G-index theory and degree of G-equivariant mapsNorbil Leodan Cordova Neyra 07 May 2010 (has links)
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] / 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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