dc.contributorVendrúscolo, Daniel
dc.contributorhttp://lattes.cnpq.br/8602232587914830
dc.contributorUribe, Oscar Eduardo Ocampo
dc.contributorhttp://lattes.cnpq.br/7834219229605868
dc.contributorhttp://lattes.cnpq.br/5286474662045113
dc.creatorDiniz, Renato dos Santos
dc.date.accessioned2021-04-19T11:12:57Z
dc.date.accessioned2022-10-10T21:35:08Z
dc.date.available2021-04-19T11:12:57Z
dc.date.available2022-10-10T21:35:08Z
dc.date.created2021-04-19T11:12:57Z
dc.date.issued2020-12-07
dc.identifierDINIZ, Renato dos Santos. Grupos de tranças de superfícies finitamente perfuradas e grupos cristalográficos. 2020. Tese (Doutorado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2020. Disponível em: https://repositorio.ufscar.br/handle/ufscar/14134.
dc.identifierhttps://repositorio.ufscar.br/handle/ufscar/14134
dc.identifier.urihttp://repositorioslatinoamericanos.uchile.cl/handle/2250/4044363
dc.description.abstractThe 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.
dc.languagepor
dc.publisherUniversidade Federal de São Carlos
dc.publisherUFSCar
dc.publisherPrograma de Pós-Graduação em Matemática - PPGM
dc.publisherCâmpus São Carlos
dc.rightshttp://creativecommons.org/licenses/by-nc-nd/3.0/br/
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Brazil
dc.subjectGrupo de tranças de superfícies finitamente perfuradas
dc.subjectGrupos cristalográficos
dc.subjectSubgrupo de torção
dc.subjectClasse de conjugação de elementos de ordem finita
dc.subjectBraid groups on finitely punctured surfaces
dc.subjectCrystallographic groups
dc.subjectTorsion subgroup
dc.subjectConjugacy classes of finite order elements
dc.titleGrupos de tranças de superfícies finitamente perfuradas e grupos cristalográficos
dc.typeTesis


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