Computations of parabolic character schemes of knots

Yunhi Cho; Hyuk Kim; Seonhwa Kim; Seokbeom Yoon

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arXiv · 2608.06890

Computations of parabolic character schemes of knots

Yunhi Cho·Hyuk Kim·Seonhwa Kim·Seokbeom Yoon

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Abstract

We compute parabolic $\mathrm{SL}_2(\mathbb{C})$-character schemes of knots using the parabolic quandle. To this end, we introduce sign-refined arc-colorings and show that their sign data encode the obstruction classes of the induced parabolic representations. We also establish a correspondence between the schemes defined by sign-refined arc-colorings and the parabolic character scheme. This yields a practical diagrammatic method for computing complete lists of parabolic characters, together with their multiplicities and obstruction classes. Using this method, we verify a conjecture of B\'{e}nard and Detcherry for all small knots with at most $12$ crossings.

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BibTeX RIS

Yunhi Cho, Hyuk Kim, Seonhwa Kim, Seokbeom Yoon. 2026-08-07. Computations of parabolic character schemes of knots. https://arxiv.org/abs/2608.06890

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