On the Khovanov homology of 3-braids

Abstract

We prove the conjecture of Przytycki and Sazdanović that the Khovanov homology of the closure of a 3-stranded braid only contains torsion of order 2. This conjecture has been known for six out of seven classes in the Murasugi-classification of 3-braids, and we show it for the remaining class. Our proof also works for the other classes and relies on Bar-Natan’s version of Khovanov homology for tangles as well as his delooping and cancellation techniques and the reduced integral Bar-Natan–Lee–Turner spectral sequence. We also show that the Knight move conjecture holds for 3-braids.