Partially abelian representations of knot groups

Yunhi Cho, Seokbeom Yoon

Research output: Contribution to journalArticlepeer-review


A knot complement admits a pseudo-hyperbolic structure by solving Thurston’s gluing equations for an octahedral decomposition. It is known that a solution to these equations can be described in terms of region variables, also called w-variables. In this paper, we consider the case when pinched octahedra appear as a boundary parabolic solution in this decomposition. The w-solution with pinched octahedra induces a solution for a new knot obtained by changing the crossing or inserting a tangle at the pinched place. We discuss this phenomenon with corresponding holonomy representations and give some examples including ones obtained from connected sum.

Original languageEnglish
Pages (from-to)239-250
Number of pages12
JournalBulletin of the Korean Mathematical Society
Issue number1
StatePublished - 2018


  • Boundary parabolic representation
  • Knot diagram change


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