SIGMA 22 (2026), 050, 22 pages      arXiv:2505.01398      https://doi.org/10.3842/SIGMA.2026.050

Extending Knot Polynomials of Braided Hopf Algebras to Links

Stavros Garoufalidis ^a, Matthew Harper ^b, Ben-Michael Kohli ^c, Jiebo Song ^d and Guillaume Tahar ^d
a) International Center for Mathematics, Department of Mathematics, Southern University of Science and Technology, Shenzhen, P.R. China
^b) Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
^c) Section de Mathématiques, Université de Genève, rue du Conseil-Général 7-9, 1205 Genève, Switzerland
^d) Beijing Institute of Mathematical Sciences and Applications, Beijing, P.R. China

Received October 20, 2025, in final form May 10, 2026; Published online May 18, 2026

Abstract
Recently, a plethora of multivariable knot polynomials were introduced by Kashaev and one of the authors, by applying the Reshetikhin-Turaev functor to rigid $R$-matrices that come from braided Hopf algebras with automorphisms. We study the extension of these knot invariants to links, and use this to identify some of them with known link invariants, as conjectured in that same recent work.

Key words: knots; links; Nichols algebras; Links-Gould polynomial; $R$-matrices.

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