Mathematical Research Letters

Volume 26 (2019)

Number 3

Khovanov width and dealternation number of positive braid links

Pages: 627 – 641



Sebastian Baader (Mathematisches Institut, Universität Bern, Switzerland)

Peter Feller (Eidgenössische Technische Hochschule (ETH) Zürich, Switzerland)

Lukas Lewark (Mathematisches Institut, Universität Bern, Switzerland)

Raphael Zentner (Faculty of Mathematics, University of Regensburg, Germany)


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 Ozsváth, Stipsicz, and Szabó’s Upsilon invariant, allows us to determine the exact cobordism distance between torus knots with braid index two and six.

The second and third author are grateful for support by the Swiss National Science Foundation and the Max Planck Institute for Mathematics. The fourth author is grateful for support by the SFB ‘Higher Invariants’ at the University of Regensburg, funded by the Deutsche Forschungsgemeinschaft (DFG).

Received 29 October 2016

Accepted 16 October 2018

Published 25 October 2019