In 2016, Levine showed that there exists a knot in a homology 3‐sphere which is not smoothly concordant to any knot in $S^3$ where one allows concordances in any smooth homology cobordism. Whether the same is true if one allows topological concordances is not known. One might hope that such an example might be detected by the powerful filtration of knot concordance introduced by Cochran–Orr–Teichner. We prove that this is not the case, demonstrating that for any knot in any homology sphere there is a knot in $S^3$ equivalent to the original knot modulo any term of this filtration. Our results apply equally well to link concordance. As an application, we prove that every winding number $\pm 1$ satellite operator acts bijectively on knot concordance, modulo any term of the solvable filtration.

中文翻译：

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同构球体中结的拓扑一致性和可解过滤

莱文（Levine）在2016年指出，在一个3阶同构球中存在一个结，该结与在 ${\mathrm{小号}}^3$在任何平滑的同源共融主义中，都允许有一致之处。如果允许拓扑一致，是否相同也未知。有人希望可以通过Cochran–Orr–Teichner引入的强大的结点协调过滤功能来检测到这样的例子。我们证明事实并非如此，这表明任何同源领域中的任何一个结都存在一个结${\mathrm{小号}}^3$等效于该过滤过程中任何术语的原始结。我们的结果同样适用于链接一致性。作为应用，我们证明每个绕组号$\pm \mathrm{1个}$ 卫星运营商以可解过滤的任何项为模，对结一致性进行双目行动。