Artin presentations of the trivial group and hyperbolic closed pure 3-braids

We consider a special class of framed links that arise from the hexatangle. Such links are introduced in [3], where it 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 hexatangl...

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Bibliographic Details
Published inTopology and its applications Vol. 354; p. 108989
Main Authors Armas-Sanabria, Lorena, Rodríguez Viorato, Jesús, Jasso-Hernández, E. Fanny
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.09.2024
Subjects
Artin n-presentations of the trivial group
Dehn surgery
Hexatangle
Pure 3-braids
Hexatangle
57M25
Dehn surgery
Pure 3-braids
Artin n-presentations of the trivial group
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Summary:We consider a special class of framed links that arise from the hexatangle. Such links are introduced in [3], where it 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 [4], we determine which closed pure 3-braids are hyperbolic.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2024.108989