On the periodic non-orientable 4-genus of a knot

TL;DR

This paper demonstrates that for p-periodic knots, the equivariant and non-equivariant non-orientable 4-genus can differ, highlighting a distinction from the behavior of Seifert genus in periodic knots.

Contribution

It establishes that the equivariant and non-equivariant non-orientable 4-genus can differ for p-periodic knots, contrasting with known results for Seifert genus.

Findings

Equivariant and non-equivariant non-orientable 4-genus may differ for p-periodic knots

Results extend understanding of genus invariants in knot theory

Contrasts with the agreement of Seifert genus in periodic knots

Abstract

We show that the equivariant and non-equivariant non-orientable 4-genus of p-periodic knots may differ, for any choice of p>1. 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 Edmods' acclaimed result by which the equivariant and non-equivariant Seifert genus of a periodic knot agree.