We establish homotopy ribbon concordance obstructions coming from the Blanchfield form and Levine–Tristram signatures. Then, as an application of twisted Alexander polynomials, we show that for every knot K with nontrivial Alexander polynomial, there exists an infinite family of knots that are all concordant to K and have the same Blanchfield form as K, such that no pair of knots in that family is homotopy ribbon concordant.

中文翻译：

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同伦带一致性、Blanchfield 配对和扭曲的亚历山大多项式

我们建立了来自 Blanchfield 形式和 Levine-Tristram 签名的同伦带状索引障碍。然后，作为扭曲亚历山大多项式的应用，我们证明对于每个具有非平凡亚历山大多项式的节点K，存在一个无限的节点家族，它们都与K一致并且具有与K相同的布兰奇菲尔德形式，因此没有一对节点在那个家族是同伦丝带一致的。