O produto tensorial não abeliano de grupos e aplicações

• Autor(a) principal: Figueiredo, Gustavo Cazzeri Innocencio
• Data de Publicação: 2015
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFSCAR
• Texto Completo: https://repositorio.ufscar.br/handle/ufscar/7468
• topic: Produto tensorial não-abeliano; Teoria de homotopia; Funtor quadrático universal de Whitehead; Nonabelian tensor product; Whitehead universal quadratic functor; Homotopy theory; CIENCIAS EXATAS E DA TERRA::MATEMATICA

The nonabelian tensor square GG of a group G was introduced by R. K. Dennis [8] in a search for new homology functors having a close relationship to K-theory and it is based on the work of C. Miller [14]. Subsequently R. Brown and J.-L. Loday [6] discovered a topological significance for the tensor square, namely, that the third homotopy group of the suspension of an Eilenberg MacLane space K(G; 1) satisfies _3 �����SK(G; 1) _ _= ker(_1), where _1 : GG ! G is the “comutator homomorphism”: _1(gh) = [g; h] = ghg�����1h�����1, 8g; h 2 G. They also defined the tensor product GH of two distinct groups acting “compatibly” on each other and showed that it arose in a certain “universal crossed square”. The main purpose of this work is to present the first properties of the nonabelian tensor product of groups and its applications in homotopy theory.