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Doctoral Thesis
DOI
10.11606/T.55.2013.tde-01042013-102842
Document
Author
Full name
Ana Paula Tremura Galves
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2013
Supervisor
Committee
Manzoli Neto, Oziride (President)
Andrade, Maria Gorete Carreira
Hartmann Júnior, Luiz Roberto
Mattos, Denise de
Monis, Thais Fernanda Mendes
Title in Portuguese
Decomposição celular e torção de Reidemeister para formas espaciais esféricas tetraedrais
Keywords in Portuguese
Anel de cohomologia
Decomposição celular
Formas espaciais esféricas
Grupo binário tetraedral
Região fundamental
Torção de Reidemeister
Abstract in Portuguese
Dada uma ação isométrica livre do grupo binário tetraedral G sobre esferas de dimensão ímpar, obtemos uma decomposição celular finita explícita para as formas espaciais esféricas tetraedrais, fazendo uso do conceito de região (ou domínio) fundamental. A estrutura celular deixa explícita uma descrição do complexo de cadeias sobre o grupo G. Como aplicações, utilizamos o complexo de cadeias e a interpretação geométrica do produto cup para calcular o anel de cohomologia da forma espacial esférica tetraedral em dimensão três, e também calculamos a torção de Reidemeister destes espaços para uma determinada representação de G
Title in English
Cellular decomposition and Reidemeister torsion for tetrahedral spherical space forms
Keywords in English
Binary tetrahedral group
Cellular decomposition
Cohomology ring
Fundamental domain
Reidemeister torsion
Spherical space forms
Abstract in English
Given a free isometric action of a binary tetrahedral group G on odd dimensional spheres, we obtain an explicit finite cellular decomposition of the tetrahedral spherical space forms, using the concept of fundamental domain. The cellular structure gives an explicit description of the associated cellular chain complex over the group G. As applications we use the chain complex and the geometric interpretation of the cup product to calculate the cohomology ring of the tetrahedral spherical space form in three dimension, and also compute the Reidemeister torsion of these spaces for a determined representation of G
 
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Publishing Date
2013-04-01
 
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