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Doctoral Thesis
DOI
https://doi.org/10.11606/T.55.2018.tde-26042018-112012
Document
Author
Full name
Rui Marcos de Oliveira Barros
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1995
Supervisor
Committee
Manzoli Neto, Oziride (President)
Cruz, Ricardo Nogueira da
Daccach, Janey Antonio
Hacon, Derek Douglas Jack
Saeki, Osamu
Title in Portuguese
VARIEDADES SATÉLITES
Keywords in Portuguese
Não disponível
Abstract in Portuguese
Seja f : Fk → Sk+2 um mergulho de uma variedade orientada fechada Fk em uma esfera (k + 2)-dimensional Sk+2. Denotemos por V uma vizinhança tubular aberta de f (Fk ). Neste trabalho construimos em V uma variedade k-dimensional M que é o espaço total de um recobrimento de n folhas de Fk . Esta construção generaliza a construção de satélites de nós clássicos, por isso chamamos M de variedade satélite de Fk. Usando a variedade de Seifert W do mergulho f (Fk ), mostramos que existe variedade de Seifert S para o mergulho satélite g : M → V ⊂ Sk+2 tal que em Sk+2 - V a variedade S é formada por n cópias paralelas de W. Utilizando a variedade S conseguimos fazer uma decomposição no espaço total Xm do recobrimento cíclico infinito do complementar Xm = Sk+2 - g(M). Esta decomposição possibilita comparar os módulos de Alexander H*(XM) do satélite, com os módulos H*(XF) do mergulho inicial. Apresentamos no início do trabalho uma caracterização algébrica dos módulos de Alexander para mergulhos de superfícies orientadas fechadas F2 em uma esfera S4. Utilizando essa caracterização calculamos os módulos de Alexander de alguns exemplos de construção de satélites bidimensionais.
Title in English
Satellite manifolds
Keywords in English
Not available
Abstract in English
Let VFΦFk x D2 be a trivialization by Φ of a tubular neighborhood of an embedding of an orientable manifold Fk in Sk+2. In this work we define embeddings of certain manifolds Mk in VF. These manifolds are defined in such way that the map π :VFφFk x D2 → Fk restricted to Mk is an n-covering map of Fk. We call these manifolds satellites of Fk since it is a generalization of a satellite construction in the classical case. We prove that there exists a Seifert Manifold Wk+1 for Mk built of n-parallel copies of a Seifert Manifold for Fk outside VF. Using Wk+1 it is possible to relate many invariants of the embeclding of Fk with those of the embedding of the manifold Mk. In particular we study the relation between the Alexander Modules of the two embeddings using a special decomposition of the Abelian Covering XM of Sk+2 - VM(VM≅M x D2). For the case of orientable surfaces in S4 we are able to get more informations and examples.
 
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RuiMarcosOBarros.pdf (47.05 Mbytes)
Publishing Date
2018-04-26
 
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