Divide knots of maximal genus defect

Abstract

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.

9 pages, 5 figures

References in corpus (2)

• On the topological 4-genus of torus knots
• A sharp signature bound for positive four-braids