On the topological 4-genus of torus knots

Abstract

We prove that the topological locally flat slice genus of large torus knots takes up less than three quarters of the ordinary genus. As an application, we derive the best possible linear estimate of the topological slice genus for torus knots with non-maximal signature invariant.

19 pages, 4 figures. Second version: minor changes, accepted for publication by Transactions of the AMS