The ${\rm SL}(2,\mathbb{C})$-character variety of $8_{18}$

Haimiao Chen

doi:10.1007/s40840-025-01952-z

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arXiv · 2508.12203

The ${\rm SL}(2,\mathbb{C})$-character variety of $8_{18}$

Haimiao Chen

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Abstract

The knot $8_{18}$ is the first non-arborescent hyperbolic knot. In 2020, Paoluzzi and Porti found its ${\rm SL}(2,\mathbb{C})$-character variety with the aid of a computer, but many details were omitted. In this paper, we determine the character variety by a software-free procedure, which is easy to follow and enlightening. Along the way, we develop an efficient method for working with simultaneous conjugacy classes of four elements of ${\rm SL}(2,\mathbb{C})$.

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BibTeX RIS

Haimiao Chen. 2025-08-17. The ${\rm SL}(2,\mathbb{C})$-character variety of $8_{18}$. https://doi.org/10.1007/s40840-025-01952-z

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