2023/06/16 by Lorena Armas-Sanabria, Armas-Sanabria, Lorena, Jesús Rodríguez-Viorato +3
Mathematics · #57M25 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2306.09636
openalex publication_date 2023/06/16 · openalex created_date 2023/06/20 · openalex updated_date 2026/07/28
We consider a special class of framed links that arise from the hexatangle. Such links are introduced in [arXiv:0807.1677], which was also analyzed when the 3-manifold obtained after performing integral Dehn surgery on closed pure 3-braids is S3. In the present paper, we analyze the symmetries of the hexatangle and give a list of Artin n-presentations for the trivial group. These presentations correspond to the double-branched covers of the hexatangle that produce S3 after Dehn surgery. Also, using a result of Birman and Menasco (1994), we determine which closed pure 3-braids are hyperbolic.