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Master's Dissertation
DOI
10.11606/D.55.2007.tde-18062007-143128
Document
Author
Full name
Luciana Vale Silva
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2007
Supervisor
Committee
Manzoli Neto, Oziride (President)
Dias, Ires
Libardi, Alice Kimie Miwa
Title in Portuguese
Teoria de homotopia simples e torção de Whitehead
Keywords in Portuguese
Deformações
Grupo de Whitehead
Homotopia
Homotopia simples
Torção de Whitehead
Abstract in Portuguese
Este trabalho apresenta a teoria de homotopia simples, desenvolvida por J. H. C. Whitehead, com o objetivo de obter um método para classificar espaços com o mesmo tipo de homotopia. Com esta motivação, Whitehead introduz o conceito de equivalência de homotopia simples entre complexos simpliciais, que posteriormente é generalizado para complexos CW, espaços criados pelo próprio Whitehead. Um resultado imediato desta teoria é que quando dois espaços têm o mesmo tipo de homotopia simples, eles têm o mesmo tipo de homotopia. A recíproca desta afirmação é então conjecturada. Mostraremos que trata-se de uma conjectura falsa, contudo a investigação de sua confirmação produz um material que toma rumo próprio. Nosso enfoque são os aspectos algébricos envolvidos nesta investigação
Title in English
Simple-homotopy theory and Whitehead torsion
Keywords in English
Deformations
Homotopy
Simple-homotopy
Whitehead group
Whitehead torsion
Abstract in English
This work presents the simple-homotopy theory, developed by J. H. C. Whitehead, with the goal to get an method to classify spaces with the same homotopy type. So, with this motivation, Whitehead introduced the concept of simple-homotopy equivalence between simplicial complexes, that later was generalized for CW complexes, spaces created by himself. An immediate result of this theory is that, if two spaces have the same simple-homotopy type, they have the same homotopy type. Then, the reciprocal statement is conjectured. We will show that the conjecture is not true, but the research about its truthfulness produces a material that takes its own way. Our approach are the algebraic aspects involved in this research
 
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disluciana.pdf (533.06 Kbytes)
Publishing Date
2007-06-18
 
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