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 Partially abelian representations of knot groups Bull. Korean Math. Soc. 2018 Vol. 55, No. 1, 239-250 https://doi.org/10.4134/BKMS.b160996Published online January 31, 2018 Yunhi Cho, Seokbeom Yoon University of Seoul, Seoul National University Abstract : 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. Keywords : knot diagram change, boundary parabolic representation MSC numbers : 57M25 Downloads: Full-text PDF