2024/03/20 by Lorena Armas-Sanabria, Armas-Sanabria, Lorena, Mario Eudave-Muñoz +5
Biochemistry, Genetics and Molecular Biology · Medicine · #57K10 #57M05 #Aortic Thrombus and Embolism #Autoimmune and Inflammatory Disorders #Dermatological and Skeletal Disorders #FOS: Mathematics #Geometric Topology (math.GT)
paper · pdf · doi:10.48550/arxiv.2403.13326
openalex publication_date 2024/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.