GGT seminar: An operator on bordered Khovanov homology induced by 2-cabling

Abstract: Cabling strongly invertible knots induces an operator on associated 4-ended tangles. In the case of 2-cabling, I will describe the construction of the resulting induced operator on the bordered Khovanov theory of Koteslkiy–Watson–Zibrowius, a theory that assigns immersed curves in a 4-punctured sphere to 4-ended tangles. Finally, I will discuss some of the structure revealed by this operator, in particular, how it relates to a new concordance invariant due to Lewark–Zibrowius.