Boltzmann Enhancements of Biquasile Counting Invariants

WonHyuk Choi; Deanna Needell; Sam Nelson

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arXiv · 1704.02555

Boltzmann Enhancements of Biquasile Counting Invariants

WonHyuk Choi·Deanna Needell·Sam Nelson

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Abstract

In this paper, we build on the biquasiles and dual graph diagrams introduced in arXiv:1610.06969. We introduce \textit{biquasile Boltzmann weights} that enhance the previous knot coloring invariant defined in terms of finite biquasiles and provide examples differentiating links with the same counting invariant, demonstrating that the enhancement is proper. We identify conditions for a linear function $\phi:\mathbb{Z}_n[X^3]\to\mathbb{Z}_n$ to be a Boltzmann weight for an Alexander biquasile $X$.

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WonHyuk Choi, Deanna Needell, Sam Nelson. 2017-04-09. Boltzmann Enhancements of Biquasile Counting Invariants. https://arxiv.org/abs/1704.02555

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