Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2018; 55(1): 239-250

Online first article July 11, 2017      Printed January 31, 2018

https://doi.org/10.4134/BKMS.b160996

Copyright © The Korean Mathematical Society.

Partially abelian representations of knot groups

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

Stats or Metrics

Share this article on :

Related articles in BKMS