Extending Knot Polynomials of Braided Hopf Algebras to Links

TL;DR

This paper extends knot polynomials derived from braided Hopf algebras to links and identifies some with known link invariants, building on recent developments in multivariable knot polynomials.

Contribution

It advances the theory by generalizing knot invariants to links and confirming conjectures about their relation to existing link invariants.

Findings

Extension of knot invariants to links achieved.

Identification of some invariants with known link invariants.

Supports conjectures from recent work on multivariable knot polynomials.

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.