Speaker: Marithania Silvero (Seville University)
Place/time: March 9, 2023; 5:10-6:10 room 736 Phillips Hall
Title: 4-braids and Khovanov homotopy type
Abstract: Khovanov homology is a link invariant which generalizes Jones polynomial. In general, computing the Jones polynomial (so also Khovanov homology) is NP-hard. However, if we consider a closed braid of a fixed number of strands, it is well-known that all classical quantum invariants (in particular the Jones polynomial) can be computed in polynomial time. We conjecture that the complexity of computing Khovanov homology of a closed braid of fixed number of strands is polynomial with respect to the number of crossings.
In this talk we show some advances on the conjecture, showing that computing the result holds when considering extreme Khovanov homology of closed braids of at most 4 strands. In fact, we show an algorithm to determine extreme Khovanov homotopy type of those braids in polynomial time.