Boltzmann Enhancements of Biquasile Counting Invariants

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 $\varphi :{\mathbb{Z}}_n[X^3]\to {\mathbb{Z}}_n$ to be a Boltzmann weight for an Alexander biquasile $X$.

arXiv comment10 Pages, v3 updates email addresses and corrects a few typos. To appear in JKTR

Cited by in corpus (2)

• Niebrzydowski Algebras and Trivalent Spatial Graphs
• Biquasile Colorings of Oriented Surface-Links