On Khovanov Homology of Quasi-Alternating Links

We prove that the length of any gap in the differential grading of the Khovanov homology of any quasi-alternating link is one. As a consequence, we obtain that the length of any gap in the Jones polynomial of any such link is one. This establishes a weaker version of Conjecture 2.3 in (Topol Appl 264:1–11, 2019). Moreover, we obtain a lower bound for the determinant of any such link in terms of the breadth of its Jones polynomial. This establishes a weaker version of Conjecture 3.8 in (Algebr Geom Topol 15:1847–1862, 2015). The main tool in obtaining this result is establishing the Knight Move Conjecture [(Algebr Geom Topol 2:337-370, 2002), Conjecture 1] for the class of quasi-alternating links.