Grupos de tranças de superfícies finitamente perfuradas e grupos cristalográficos

Detalhes bibliográficos
Ano de defesa: 2020
Autor(a) principal: Diniz, Renato dos Santos
Orientador(a): Vendrúscolo, Daniel lattes
Banca de defesa: Não Informado pela instituição
Tipo de documento: Tese
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Universidade Federal de São Carlos
Câmpus São Carlos
Programa de Pós-Graduação: Programa de Pós-Graduação em Matemática - PPGM
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Palavras-chave em Inglês:
Área do conhecimento CNPq:
Link de acesso: https://repositorio.ufscar.br/handle/20.500.14289/14134
Resumo: The link between braid groups on surfaces and crystallographic groups has become such an interesting topic. In the last years some advances were found in the studies of this relation, specially in the case of Artin braid groups and braid groups on closed surfaces (orientable or non-orientable). Our thesis work was strongly inspired by the works in [39] and [42], since here we finish the last cases about surfaces, to which we could ask: is there a relation between braid groups on surfaces and crystallographic groups? Here we analyse, with details, the interaction between braid groups on closed surfaces (orientable or non-orientable) with a finite number of points removed and crystallographic groups. Let X be a closed and finitely punctured surface (orientable or non-orientable). We present new results when X is a closed and finitely punctured surface (orientable or non-orientable) that has a link with crystallographic groups. We prove that the quotient group $B_n(X)\P'_n(X)$ is a crystallographic group, we characterize the finite order elements, i. e., we analyse its torsion subgroup and study the conjugacy classes of the finite order elements. When X is a non-orientable closed and finitely punctured surface with genus $g \geq 2$, we calculate a presentation for the braid groups $P_n(X)$ and $B_n(X)$. In the case of $Pn(X)$, we couldn't find any other presentation in the literature.