The Non-Orientable Four-Genus of Ten-Crossing Knots

Abstract

We perform a detailed and complete computation of the non-orientable smooth 4-genus gamma4 for all 165 prime knots with crossing number equal to ten. Prior to this work, this important knot invariant was only known for knots with up to 9 crossings, and our work substantially expands on this body of knowledge. Our results have been published in the peer-reviewed Journal of Knot Theory and its Ramifications, and have been entered into the online database of knot invariants for low-crossing knots - KnotInto