Positive Artin Presentations

Lorena Armas-Sanabria; Mario Eudave-Muñoz; Juan Pablo Díaz-González; Gabriela Hinojosa-Palafox

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arXiv · 2403.13326

Positive Artin Presentations

Lorena Armas-Sanabria·Mario Eudave-Muñoz·Juan Pablo Díaz-González·Gabriela Hinojosa-Palafox

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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.

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BibTeX RIS

Lorena Armas-Sanabria, Mario Eudave-Muñoz, Juan Pablo Díaz-González, Gabriela Hinojosa-Palafox. 2024-03-20. Positive Artin Presentations. https://arxiv.org/abs/2403.13326

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