Equivariant cobordisms between 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.