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Bibliographic Details
Main Authors: Armas-Sanabria, Lorena, Eudave-Muñoz, Mario, Díaz-González, Juan Pablo, Hinojosa-Palafox, Gabriela
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2403.13326
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Table of Contents:
  • An integral framed, closed pure n-braid B' in the 3-sphere describes a positive Artin presentation, if the braid B can be put on a disk with holes such that each relation describes a positive path and these paths are disjoint. In the present paper we classify the closed, pure n-braids B' in the 3-sphere, such that B represents a positive Artin presentation. Also we prove that if such B describes a positive Artin presentation then B' is strongly invertible. Such positive Artin presentation give us the fundamental group of closed, connected and orientable 3-manifolds M, and in fact, by giving an example, we show that there exist 3-manifolds whose fundamental group does not admit a positive Artin presentation.