Boltzmann Enhancements of Biquasile Counting Invariants
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 $X$.
PDF AbstractCode
Categories
Geometric Topology
Quantum Algebra
57M25, 57M27
