The \rm SL(2,ℂ)-character variety of an arborescent knot

2023/04/20 by Chen, Haimiao
#57K10 #57K31 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2304.10345

Abstract

We clarify steps for determining the \rm SL(2,ℂ)-character variety of any arborescent knot. Interestingly, we show that the `excellent parts' of arborescent knots K₁,K₂ are isomorphic if K₁ can be related to K₂ through certain moves on projection diagrams. Furthermore, we give a sufficient condition in terms of diagram for the existence of components of dimension larger than 1. A generalization to arborescent links is sketched.

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