Biquandles, quivers and virtual bridge indices

Tirasan Khandhawit; Puttipong Pongtanapaisan; Brandon Wang

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arXiv · 2504.10396

Biquandles, quivers and virtual bridge indices

Tirasan Khandhawit·Puttipong Pongtanapaisan·Brandon Wang

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Abstract

We investigate connections between biquandle colorings, quiver enhancements, and several notions of the bridge numbers $b_i(K)$ for virtual links, where $i=1,2$. We show that for any positive integers $m \leq n$, there exists a virtual link $K$ with $b_1(K) = m$ and $b_2(K) = n$, thereby answering a question posed by Nakanishi and Satoh. In some sense, this gap between the two formulations measures how far the knot is from being classical. We also use these bridge number analyses to systematically construct families of links in which quiver invariants can distinguish between links that share the same biquandle counting invariant.

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Tirasan Khandhawit, Puttipong Pongtanapaisan, Brandon Wang. 2025-04-14. Biquandles, quivers and virtual bridge indices. https://arxiv.org/abs/2504.10396

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