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Master's Dissertation
DOI
10.11606/D.55.2018.tde-09042018-144744
Document
Author
Full name
Silvia Regina Vieira da Silva
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1995
Supervisor
Committee
Manzoli Neto, Oziride (President)
Loibel, Gilberto Francisco
Pergher, Pedro Luiz Queiroz
Title in Portuguese
MERGULHOS EM CODIMENSAO 1 E GENUS DE VARIEDADES
Keywords in Portuguese
Não disponível
Abstract in Portuguese
O objetivo deste trabalho é estudar a generalização natural de genus de uma variedade de qualquer dimensão e seu relacionamento com o genus de π1(M) . O genus de uma variedade compacta e conexa m-dimensional M é o número máximo de subvariedades de codimensão 1 , conexas , disjuntas com colarinho duplo que não desconecta M e o genus de um grupo G é o maior inteiro r tal que existe epimorfismo de G em F , onde Fr é o grupo livre com r geradores. O trabalho é baseado no artigo " The genus and the fundamental group of hight dimensional manifolds " , cujo autor é Octav Cornea . Mostra-se vários resultados , em particular temos que genus(M) ≤ genus(π1(M)), valendo a igualdade se o bordo de M for vazio. Também fazemos uma classificação de enlaçamentos de circunferências numa superfície orientável de genus g qualquer.
Title in English
Codimension one embeddings and genus of manifold
Keywords in English
Not available
Abstract in English
The purpose of this work is a natural generalization of the concept of the genus of a manifold M of any dimension and its relationship to the genus of π1 ( M) . The genus of a m-dimensional , compact , connected manifold M is the maximum number of disjoint , connected , codimension one biccolared submanifolds that do not disconected M and the genus of a group G is the maximum integer r such that we can find an epimorfismo from G to Fr , where Fr is a free group of rank r. The basic reference for this work is the article "The genus and the group fundamental of hight dimensional manifolds" by Octav Cornea . Many results are developed in particular we have genus (M) ≤ genus (π1 ( M)) and for ∂M = ∅ the equalit holds . We also establish a classification for links of g componentes on a orientable surface of genus g, for any g.
 
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SilviaReginaVieira.pdf (24.29 Mbytes)
Publishing Date
2018-04-09
 
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