From planar to annular to toroidal bracket polynomials for pseudo knots and links
Geometric Topology
2025-08-20 v2
Abstract
Pseudo links are equivalence classes under Reidemeister-type moves of link diagrams containing crossings with undefined over and under information. In this paper, we extend the Kauffman bracket and Jones-type polynomials from planar pseudo links to annular and toroidal pseudo links and their respective lifts from the three-space to the solid torus and the thickened torus. Moreover, since annular and toroidal pseudo links can be represented as mixed links in the three-sphere, we also introduce the respective Kauffman bracket and Jones-type polynomials for their planar mixed link diagrams. Our work provides new tools for the study of annular and toroidal pseudo links.
Cite
@article{arxiv.2501.00736,
title = {From planar to annular to toroidal bracket polynomials for pseudo knots and links},
author = {Ioannis Diamantis and Sofia Lambropoulou and Sonia Mahmoudi},
journal= {arXiv preprint arXiv:2501.00736},
year = {2025}
}