Universal Link Invariant via Configuration Spaces

par Cristina Anghel (LBMP, Univ. Clermont Auvergne)

mercredi 27 mai 2026, 11:45 → 12:45 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Seed Seminar of Mathematics and Physics

Spring '26: TQFT and Knot Theory 

Coloured Jones and Alexander polynomials are quantum invariants originating in representation theory and their geometric information is an important open problem in quantum topology. We present a new topological perspective that unifies these invariants through the topology of configuration spaces. First, for a fixed N, we define new link invariants: “N th Unified Jones invariant” and “N th Unified Alexander invariant” globalising all coloured Jones and ADO link polynomials of (multi)-colours bounded by N. Asymptotically, Habiro defined his universal knot invariant globalising coloured Jones polynomials by introducing the Habiro ring. For the link case, such globalisation remained open for both sequences of invariants.

We answer this problem coming from representation theory using topological tools. On the representation theory side we define extensions of Habiro type rings. On the topological side, we construct a universal Jones link invariant and a universal Alexander link invariant. Putting these together, our universal invariants of geometrical nature take values in the extended Habiro rings that we construct.

More information: https://seedseminar.apps.math.cnrs.fr/program/#may-27-2026

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