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The ${\rm SL}(2,\mathbb{C})$-character variety of an arbo...
[Submitted on 20 Apr 2023 (v1), last revised 23 Jun 2026 (this v · 2026-06-24 · via math updates on arXiv.org

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Abstract:We describe a procedure for computing the ${\rm SL}(2,\mathbb{C})$-character variety of an arborescent knot. Along the way, we clarify several facts about representations of arborescent tangles. Then we study a family of hyperbolic knots whose exteriors contain closed essential surfaces, showing that each of these knots has $1$-dimensional character variety. This provides infinitely many positive answers to a question of Boyer and Zhang posed in 1998.

Submission history

From: Haimiao Chen [view email]
[v1] Thu, 20 Apr 2023 14:34:06 UTC (213 KB)
[v2] Sat, 2 Mar 2024 12:58:41 UTC (130 KB)
[v3] Tue, 23 Jun 2026 11:39:26 UTC (230 KB)