A new invariant of equivariant concordance and results on 2-bridge knots

TL;DR

This paper introduces a new invariant for equivariant concordance of strongly invertible knots, provides formulas for butterfly polynomials of two-bridge knots, and proves their infinite equivariant concordance order.

Contribution

It presents a novel invariant for equivariant concordance and applies it to demonstrate that all two-bridge knots have infinite equivariant concordance order.

Findings

No two-bridge knot is equivariantly slice.

The new invariant obstructs equivariant sliceness.

All two-bridge knots have infinite equivariant concordance order.

Abstract

We study the equivariant concordance classes of two-bridge knots, providing an easy formula to compute their butterfly polynomial, and we give two different proofs that no two-bridge knot is equivariantly slice. Finally, we introduce a new invariant of equivariant concordance for strongly invertible knots. Using this invariant as an obstruction we strengthen the result on two-bridge knots, proving that their equivariant concordance order is always infinite.