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Ordering homotopy string links over surfaces and a presentation for the generalized string links over surfaces / Ordenando os grupos de homotopia de enlaçamentos de intervalos em supefícies e uma apresentação para os grupos de homotopia de enlaçamentos de intervalos em superfíciesLima, Juliana Roberta Theodoro de 13 October 2014 (has links)
In this work, we prove that the set of link-homotopy classes of generalized string links over a closed, connected and orientable surface M of genus g ≥ 1 form a group, denoted by Bn(M) and we find a presentation for it. Moreover, we prove that its normal subgroup PBnn(M), namely, the homotopy string links over M, is bi-orderable. These results extend results proved by Juan GonzalezMeneses in [GM], [GM2] and Ekaterina Yurasovskaya in [Y], respectively. Also, we obtain an exact sequence for link-homotopy braid groups, which is an extension of [Go, Theorem 1]. / Sem resumo
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Ordering homotopy string links over surfaces and a presentation for the generalized string links over surfaces / Ordenando os grupos de homotopia de enlaçamentos de intervalos em supefícies e uma apresentação para os grupos de homotopia de enlaçamentos de intervalos em superfíciesJuliana Roberta Theodoro de Lima 13 October 2014 (has links)
In this work, we prove that the set of link-homotopy classes of generalized string links over a closed, connected and orientable surface M of genus g ≥ 1 form a group, denoted by Bn(M) and we find a presentation for it. Moreover, we prove that its normal subgroup PBnn(M), namely, the homotopy string links over M, is bi-orderable. These results extend results proved by Juan GonzalezMeneses in [GM], [GM2] and Ekaterina Yurasovskaya in [Y], respectively. Also, we obtain an exact sequence for link-homotopy braid groups, which is an extension of [Go, Theorem 1]. / Sem resumo
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