Satellites of infinite rank in the smooth concordance group

We conjecture that satellite operations are either constant or have infinite rank in the concordance group. reduce this to difficult case of winding number zero satellites, and use $SO(3)$ gauge theory provide a general criterion sufficient for image operation generate an subgroup smooth group $\mathcal{C}$. Our applies widely; notably many unknotted patterns which corresponding operators on topological zero. raise some questions conjectures regarding their interaction with concordance.