Khovanov width and dealternation number of positive braid links
  We give asymptotically sharp upper bounds for the Khovanov width and the dealternation number of positive braid links, in terms of their crossing number. The same braid-theoretic technique, combined with Ozsv\'ath, Stipsicz, and Szab\'o's Upsilon invariant, allows us to determine the exact cobordism distance between torus knots with braid index two and six. 
Sebastian Baader, Peter Feller, Lukas Lewark, Raphael Zentner
math.GT