Equivalence of two notions of equivariant concordance

Determine whether the two definitions of equivariant concordance for directed strongly invertible knots—the general extension of the strong inversion across S^3 × [0,1] versus the extension isotopic to standard rotation by π in each slice—induce the same equivalence relation on the set of directed strongly invertible knots.

Background

The paper discusses two closely related notions of equivariant concordance for directed strongly invertible knots: one allowing a general involution extension over the cobordism, and a more restrictive one where the extension is isotopic to the standard rotation by π about a fixed axis in each slice.

The relationship between these two equivalence relations affects how invariants like s_tau behave and which category of equivariant concordance they detect.