q-Rationals, link invariants and webs

We investigate the role of q-rationals in the context of link invariants. This leads us to introduce and study web categories that q-deform Deligne’s categories.

💡 Research Summary

The paper investigates how the recently introduced notion of q‑rationals can be employed to interpolate link invariants that are traditionally defined only for integer quantum dimensions. Starting from the classical setting, the authors recall that the Alexander, Jones, and HOMFLY‑PT polynomials can be obtained from skein relations and that the HOMFLY‑PT polynomial admits a quantum group interpretation via the Reshetikhin‑Turaev construction for the quantum group U_q(gl_n). In that framework the quantum integer