Equivariant cobordisms between freely-periodic knots

TL;DR

This paper classifies when freely periodic knots can bound equivariant surfaces in the 4-ball, using homology classes in lens spaces and d-invariants, providing a numerical criterion for torus knots.

Contribution

It introduces a classification of freely periodic knots bounding equivariant surfaces in the 4-ball based on homology and d-invariants, with a new numerical condition for torus knots.

Findings

Homology cobordism classification of lens spaces using d-invariants.

Numerical condition for free periods of torus knots.

Classification of equivariant surfaces in the 4-ball for freely periodic knots.

Abstract

We consider free symmetries on cobordisms between knots. We classify which freely periodic knots bound equivariant surfaces in the 4-ball in terms of corresponding homology classes in lens spaces. A key tool is the homology cobordism classification of lens spaces using d-invariants. We give a numerical condition determining the free periods for which torus knots bound equivariant surfaces in the 4-ball.