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

• Main Author: Lima, Juliana Roberta Theodoro de
• Other Authors: Mattos, Denise de
• Format: Others
• Language: en
• Published: Biblioteca Digitais de Teses e Dissertações da USP 2014
• Subjects: 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
• Online Access: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-28042015-155522/

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