New quantum invariants of planar knotoids (Q6109383)

This paper studies the classification of planar knotoids (immersions of the unit interval in \(\mathbb R^2\)) and can be considered as a follow-up paper to the first author's paper [Commun. Math. Phys. 393, No. 2, 1035--1061 (2022; Zbl 07549414)]. The invariants discussed in the paper are invariants for biframed knotoids, that are planar knotoids considered up to an equivalence relation induced by the Reidemeister II and III moves and a weak version of the Reidemeister I move, and with parallel tangent directions on the endpoint arcs. The paper manages to improve the classification table of prime knotoids given by \textit{D. Goundaroulis} et al. [``A systematic classification of knotoids on the plane and on the sphere'', Preprint, \url{arXiv:1902.07277}].