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arXiv · 2501.00736

From planar to annular to toroidal bracket polynomials for pseudo knots and links

Ioannis Diamantis·Sofia Lambropoulou·Sonia Mahmoudi
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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.

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Ioannis Diamantis, Sofia Lambropoulou, Sonia Mahmoudi. 2025-08-19. From planar to annular to toroidal bracket polynomials for pseudo knots and links. https://arxiv.org/abs/2501.00736

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