This paper demonstrates an approach for developing a framework to produce invariants of base-point-free generic spherical curves under some chosen local moves from Reidemeister moves using based chord diagrams. Our invariants not only contain Arnold's classical generic spherical curve invariant but also new invariants.
"Based chord diagrams of spherical curves." Kodai Math. J. 41 (2) 375 - 396, June 2018. https://doi.org/10.2996/kmj/1530496848