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GGD/GEAR/Quantum Topology Seminar: Genus bounds from twisted Drinfeld doubles

Event Type
wifi event
Mar 3, 2022   12:00 - 1:00 pm   Central
Daniel Lopez Neumann (Indiana University)
Eric Samperton

It is a classical result that the degree of the Alexander polynomial gives a lower bound to the Seifert genus. This theorem does not hold, however, for the Jones polynomial and other quantum knot invariants.

In this talk, we will explain how to build quantum knot polynomials that do satisfy a genus bound. Our construction relies on the "twisted" (or equivariant) Reshetikhin-Turaev construction specialized at the twisted Drinfeld double of a Z-graded Hopf algebra H, or equivalently, a relative Drinfeld center of a crossed product. When H is an exterior algebra, our invariant generalizes twisted Alexander polynomials, hence our theorem recovers Friedl-Kim's genus bounds. This is work in progress with Roland van der Veen.

Meeting ID: 881 6087 3184

Password: PSL27

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