Applications of the twisted Drinfeld double construction

Roland van der Veen (university of Groningen)

Abstract: In joint work with Daniel Lopez Neumann we showed how the quantum invariants arising from the twisted double yield a lower bound for the knot genus. We will give an elementary sketch of the construction and discuss further applications.

Bonus material:

• A handout is available here
• Two related papers joint with Daniel Lopez Neumann:
  • Genus bounds from unrolled quantum groups at roots of unity
  • Genus bounds for twisted quantum invariants
• Picture of a 2013 trip with Stavros to Ankor-Wat.
• Simple implementation of the invariant discussed in the talk.
• Most of the ideas for the implementation are due to Bar-Natan see for example this paper.