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

中文翻译：

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平滑索引组中无限等级的卫星

我们推测卫星操作在一致性组中要么是恒定的，要么是无限的。我们将此简化为绕数为零的卫星的困难情况，并使用 $SO(3)$ 规范理论为卫星操作的图像提供足以生成平滑一致性群 $\mathcal 的无限秩子群的一般准则{C}$。我们的标准广泛适用，特别是对于拓扑一致性组上的相应算子为零的未打结模式的分数。我们提出了一些关于卫星运营商及其与一致性互动的问题和猜想。