Ordering homotopy string links over surfaces and a presentation for the generalized string links over surfaces

• Autor(a) principal: Lima, Juliana Roberta Theodoro de
• Data de Publicação: 2014
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-28042015-155522/
• topic: Apresentação para os grupos de homotopia de enlaçamentos de intervalos generalizados; Enlaçamentos de intervalos; Enlaçamentos de intervalos generalizados; Homotopy generalized string links; Homotopy string links; Ordenando grupos de homotopia de enlaçamentos de intervalos; Ordering homotopy string links over surfaces; Presentation for the homotopy generalized string over surfaces

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].