Positive Artin Presentations
Geometric Topology
2024-03-21 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2403.13326,
title = {Positive Artin Presentations},
author = {Lorena Armas-Sanabria and Mario Eudave-Muñoz and Juan Pablo Díaz-González and Gabriela Hinojosa-Palafox},
journal= {arXiv preprint arXiv:2403.13326},
year = {2024}
}
Comments
18 pages, 11 figures