Bordism invariants of colored links and topologically protected tricolorings (Q6568764)

The article under review looks into topological vortices assumed to be knots or links. In order to study the stability of these vortices against decay via topologically allowed surgeries (i.e., Reidemeister moves or reconnections), the links are endowed with colorings by elements of certain groups. In this sense, this article is a sequel to a previous article where the group at issue was the quaternion group [\textit{T. Annala} et al., ``Topologically protected vortex knots and links'', Preprint, \url{arXiv:2204.03612}]. In the present article, the group considered is the group of permutations on three elements and the colors are the transpositions, so the authors consider tricolorings of links. The main result proves that a knot or a link endowed with a tricoloring can only decay into a number of standard circles or to (tricolored) trefoils.