The quantum invariants of knots and 3-manifolds are a wide family of topological invariants coming from the theory of braided monoidal categories, and in particular, quantum groups. The Jones and HOMFLY polynomials of knots are the most studied special cases of this theory. However, it is not known how these invariants are related to classical geometric properties of knots, such as the Seifert genus or fibredness.
In this talk, I’ll propose a partial solution to this problem: quantum invariants coming from "non-semisimple" quantum groups do provide genus bounds and obstructions to fibredness. More precisely, I’ll state and show a q-deformation of the classical fibering obstruction for the Alexander polynomial. The talk doesn't assumes familiarity with quantum groups. This is joint work with Roland van der Veen.
