Speaker
Description
The Gordian distance u(K,K') between two knots K and K' is the minimal number of crossing changes needed to relate K and K'. The unknotting number u(K) of a knot K arises as the Gordian distance between K and the trivial knot. Rasmussen was the first to find a connection between Khovanov homology and u: his invariant s, extracted from Khovanov homology, yields a lower bound for the slice genus and, as a consequence, for u(K). In this talk, I will introduce a new invariant λ, extracted from a universal version of Khovanov homology. Although it is not connected to the slice genus, λ is a lower bound for u, and in fact the inequality |s(K)| ≤ 2λ(K) always holds. Moreover, λ displays relations to a generalization of u, the proper rational Gordian distance. This is joint work with L. Lewark and C. Zibrowius.
