RNA foldings, Oriented Stuck Knots and State Sum Invariants

TL;DR

This paper introduces new polynomial invariants for stuck links and RNA foldings by extending quandle cocycle invariants, providing explicit computations and broadening the tools for topological and biological structure analysis.

Contribution

It extends quandle cocycle invariants to stuck links and RNA foldings, defining new polynomial invariants with explicit computational methods.

Findings

Defined single-variable and two-variable polynomial invariants for stuck links.

Extended invariants to RNA foldings and provided explicit calculations.

Demonstrated the effectiveness of new invariants through explicit examples.

Abstract

We extend the quandle cocycle invariant to the context of stuck links. More precisely, we define an invariant of stuck links by assigning Boltzmann weights at both classical and stuck crossings. As an application, we define a single-variable and a two-variable polynomial invariant of stuck links. Furthermore, we define a single-variable and two-variable polynomial invariant of arc diagrams of RNA foldings. We provide explicit computations of the new invariants.