A construction extending the Kauffman bracket polynomial and Jones-type invariants from planar pseudo links to pseudo links living in the solid torus (annular) and the thickened torus (toroidal). Pseudo links are link diagrams containing precrossings whose over/under information is undefined, taken up to generalized Reidemeister moves. The contribution defines multivariable Laurent-polynomial invariants for the annular and toroidal cases (generalizing the earlier 2-variable planar and 3-variable annular brackets), proves their invariance under the appropriate regular and full pseudo isotopy, and, via the representation of annular and toroidal pseudo links as mixed links in the three-sphere, gives corresponding bracket and Jones-type polynomials for planar mixed-link diagrams.
Pseudo links are equivalence classes, under generalized Reidemeister-type moves, of link diagrams containing precrossings: crossings whose over/under information is undefined (introduced by Hanaki to…