On the periodic non-orientable 4-genus a knot

Abstract

We show that the equivariant and non-equivariant non-orientable 4-genus of [Formula: see text]-periodic knots may differ, for any choice of [Formula: see text]. Similar results have previously been obtained for the smooth 4-genus and non-orientable 3-genus of a periodic knot. These stand in contrast to Edmonds’ acclaimed result by which the equivariant and non-equivariant Seifert genus of a periodic knot agree.