Amphichiral knots with large 4‐genus

Abstract

For each g > 0 $g>0$ we give infinitely many knots that are strongly negative amphichiral, hence rationally slice and representing 2-torsion in the smooth concordance group, yet which do not bound any locally flatly embedded surface in the 4-ball with genus less than or equal to g $g$ . Our examples also allow us to answer a question about the four-dimensional clasp number of knots.