Banca de DEFESA: PAULO CESAR CERQUEIRA DOS SANTOS JUNIOR

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
DISCENTE : PAULO CESAR CERQUEIRA DOS SANTOS JUNIOR
DATA : 11/03/2019
HORA: 09:00
LOCAL: Instituto de Matemática e Estatística
TÍTULO:

A quotient of the Artin braid group related to crystallographic groups

PALAVRAS-CHAVES:

Artin braid groups, Conjugacy classes, Crystallographic group

PÁGINAS: 65
GRANDE ÁREA: Ciências Exatas e da Terra
ÁREA: Matemática
SUBÁREA: Geometria e Topologia
ESPECIALIDADE: Topologia Algébrica
RESUMO:

Let $n\ge 3$. We studied the quotient group $B_n/[P_n, P_n]$ from the Artin braid group $B_n$ by the commutator subgroup of the Artin pure braid group $P_n$. The group $B_n/[P_n, P_n]$ is a crystallographic group that has no even-order element and has infinite elements of odd order. We also showed that there is a one-to-one correspondence between the conjugacy classes of  finite odd-order elements of $B_n/[P_n,P_n]$ with the  the conjugacy classes of  finite odd-order elements of the symmetric group $S_n$ and we realized the abelian subgroups of odd order of $S_n$ in $B_n/[P_n,P_n]$. In the case of $n=3$ we studied crystallographic subgroups of $B_3/[P_3, P_3]$ of dimension $3$. In this work we used as a main reference Gonçalves, Guaschi and Ocampo (2017). In addition to what was done in [Gonçalves, Guaschi and Ocampo 2017] , we studied the conjugacy classes of infinite order elements in $B_3/[P_3, P_3]$ and the Coxeter's quotient in $B_n/[P_n, P_n]$. 

MEMBROS DA BANCA:
Presidente - 2115559 - OSCAR EDUARDO OCAMPO URIBE
Externo à Instituição - DACIBERG LIMA GONÇALVES - USP
Externo à Instituição - JOHN GUASCHI - Caen