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We conjecture that satellite operations are either constant or have infiniterank in the concordance group. We reduce this to the difficult case of windingnumber zero satellites, and use $SO(3)$ gauge theory to provide a generalcriterion sufficient for the image of a satellite operation to generate aninfinite rank subgroup of the smooth concordance group $\mathcal{C}$. Ourcriterion applies widely; notably to many unknotted patterns for which thecorresponding operators on the topological concordance group are zero. We raisesome questions and conjectures regarding satellite operators and theirinteraction with concordance.

Satellites of Infinite Rank in the Smooth Concordance Group