RNA foldings, Oriented Stuck Knots and State Sum Invariants

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.