Partially abelian representations of knot groups

Yunhi Cho; Seokbeom Yoon

doi:10.4134/bkms.b160996

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arXiv · 1702.07878

Partially abelian representations of knot groups

Yunhi Cho·Seokbeom Yoon

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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 the decomposition. A $w$-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.

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Yunhi Cho, Seokbeom Yoon. 2017-02-25. Partially abelian representations of knot groups. https://doi.org/10.4134/bkms.b160996

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