Equivariant 4-genera of strongly invertible and periodic knots

TL;DR

This paper investigates the equivariant 4-genus of certain symmetric knots, introducing new invariants and techniques to find examples where symmetry increases the minimal genus.

Contribution

It develops new strongly invertible concordance invariants and applies Donaldson's theorem to study equivariant 4-genera, revealing cases where symmetry raises the genus.

Findings

Equivariant 4-genus can be larger than the standard 4-genus.

New invariants for strongly invertible concordance are introduced.

Several examples demonstrate the impact of symmetry on knot genus.

Abstract

We study the equivariant genera of strongly invertible and periodic knots. Our techniques include some new strongly invertible concordance group invariants, Donaldson's theorem, and the g-signature. We find many new examples where the equivariant 4-genus is larger than the 4-genus.