Communications in Analysis and Geometry

Volume 31 (2023)

Number 2

Divide knots of maximal genus defect

Pages: 367 – 379



Livio Liechti (Department of Mathematics, University of Fribourg, Switzerland)


We construct divide knots with arbitrary smooth four-genus but topological four-genus equal to one. In particular, for strongly quasipositive fibred knots, the ratio between the topological and the smooth four-genus can be arbitrarily close to zero.

Received 17 April 2020

Accepted 25 September 2020

Published 6 December 2023