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Master's Dissertation
DOI
10.11606/D.45.2009.tde-18092013-095636
Document
Author
Full name
Oscar Eduardo Ocampo Uribe
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2009
Supervisor
Committee
Goncalves, Daciberg Lima (President)
Barros, Tomas Edson
Manzoli Neto, Oziride
Title in Portuguese
Subgrupos geométricos e seus comensuradores em grupos de tranças de superfície
Keywords in Portuguese
comensurador
Grupos de tranças
grupos de tranças de superfície.
sequência de Fadell-Neuwirth
subgrupos geométricos
Abstract in Portuguese
Seja $B_mM$ o grupo de tranças com $m$ cordas sobre uma superfície $M$ e seja $N$ uma subsuperfície de $M$. Estudaremos inicialmente condições necessárias e suficientes para as quais $B_nN$ é um subgrupo de $B_mM$ ($m$ podendo ser diferente de $n$), isto é, se considerarmos a inclusão $i\colon N \to M$, queremos estabelecer condições sobre $M$ e $N$ para que a aplicação induzida $i_\ast \colon B_nN \to B_mM$ seja injetora. Em seguida, sob certas hipóteses para $N$ e $M$ calcularemos o comensurador, normalizador e centralizador de $B_nN$ em $B_mM$, sendo esse o objetivo principal desta dissertação.
Title in English
Geometric subgroups and their commensurators in surface braid groups
Keywords in English
Braid groups
commensurator
Fadell-Neuwirth sequence
geometric subgroups
surface braid groups.
Abstract in English
Let $B_m(M)$ be the braid group with $m$ strings on a surface $M$ and let $N$ be a subsurface of $M$. We will study the necessary and sufficient conditions out of which $B_n(N)$ is a subgroup of $B_m(M)$ ($m$ can be different of $n$), it means, if we consider the inclusion $i \colon N \to M$, we would like to establish conditions for $M$ and $N$ for the induced application $i_\ast \colon B_nN \to B_mM$ should be injective. After that, under some certain conditions for $M$ and $N$ we will calculate the commensurator, normalizer and centralizer of $Bn(N)$ in $Bm(M)$, being this one the principal objective of this work.
 
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Publishing Date
2013-09-25
 
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