Partially abelian representations of knot groups
| Autor: | Cho, Yunhi, Yoon, Seokbeom |
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| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Bull. Korean Math. Soc. 2018 Vol. 55, No. 1, 239--250 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.4134/BKMS.b160996 |
| Popis: | 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. Comment: 11 pages |
| Databáze: | arXiv |
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