A bound on the equivariant unknotting number

TL;DR

This paper establishes a lower bound on the equivariant unknotting number of strongly invertible knots using the equivariant signature, showing how it changes under specific equivariant moves.

Contribution

It introduces a new lower bound for the equivariant unknotting number based on the equivariant signature and analyzes its behavior under Boyle-Chen moves.

Findings

Equivariant signature provides a lower bound to three times the equivariant unknotting number.

The equivariant signature changes predictably under Boyle-Chen equivariant unknotting moves.

The absolute value of the equivariant signature is a useful invariant for bounding unknotting numbers.

Abstract

We study how the equivariant signature of strongly invertible knots changes when one of the Boyle-Chen equivariant unknotting moves is applied. It follows form our results that the absolute value of the equivariant signature introduced by Alfieri-Boyle gives a lower bound to three times the equivariant unknotting number.