Dr. Matt Hogancamp, Northeastern – The dotted Temperley-Lieb category and handle-slides

Mode: In-person

Title: The dotted Temperley-Lieb category and handle-slides

Abstract: Khovanov homology can be upgraded to an invariant of pairs (K,V) where K is a framed knot and V is an object of the dotted Temperley-Lieb category dTL. In this context, the pair (K,V) is called a colored knot, and its Khovanov invariant is called colored Khovanov homology.  In my talk I will discuss recent joint work with David Rose and Paul Wedrich, in which we construct an object in dTL (more accurately, an ind-object therein), called a Kirby color, whose associated colored Khovanov invariant satisfies the important handle-slide relation from topology. I will also give a diagrammatic description of the Kirby color, extending the presentation which defines dTL.