Grupos de tranças de superfícies finitamente perfuradas e grupos cristalográficos
Ano de defesa: | 2020 |
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Autor(a) principal: | |
Orientador(a): | |
Banca de defesa: | |
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
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Departamento: |
Não Informado pela instituição
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País: |
Não Informado pela instituição
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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. |