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Master's Dissertation
DOI
https://doi.org/10.11606/D.55.2012.tde-16042012-102241
Document
Author
Full name
Pavel Jesus Henriquez Pizarro
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2012
Supervisor
Committee
Campos, José Eduardo Prado Pires de (President)
Mattos, Denise de
Pergher, Pedro Luiz Queiroz
Title in Portuguese
Representações do grupo de tranças por automorfismos de grupos
Keywords in Portuguese
Grupo de trenzas
Grupoides
Invariantes de enlazamientos
Abstract in Portuguese
A partir de um grupo H e um elemento h em H, nós definimos uma representação : 'B IND. n' Aut('H POT. n' ), onde 'B IND. n' denota o grupo de trança de n cordas, e 'H POT. n' denota o produto livre de n cópias de H. Chamamos a a representação de tipo Artin associada ao par (H, h). Nós também estudamos varios aspectos de tal representação. Primeiramente, associamos a cada trança um grupo ' IND. (H,h)' () e provamos que o operador ' IND. (H,h)' determina um grupo invariante de enlaçamentos orientados. Então damos uma construção topológica da representação de tipo Artin e do invariante de enlaçamentos ' IND.(H,h)' , e provamos que a representação é fiel se, e somente se, h é não trivial
Title in Spanish
Representaciones ddelç grupo de trenzas por automorfismos de grupo
Keywords in Spanish
Braid group
Grupoids
Links invariantes
Abstract in Spanish
From a group H and a element h H, we define a representation : ' B IND. n' Aut('H POT. n'), where 'B IND. n' denotes the braid group on n strands, and 'H POT. n' denotes the free product of n copies of H. We call the Artin type representation associated to the pair (H, h). Here we study various aspects of such representations. Firstly, we associate to each braid a group ' IND. (H,h)' () and prove that the operator ' IND. (H,h)' determines a group invariant of oriented links. We then give a topological construction of the Artin type representations and of the link invariant ' iND. (H,h)' , and we prove that the Artin type representations are faithful if and only if h is nontrivial
 
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pavelrev.pdf (2.78 Mbytes)
Publishing Date
2012-04-16
 
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