关于缆线与对合调和不变量的注解

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-03-13 DOI:10.1112/blms.70050

Kristen Hendricks, Abhishek Mallick

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引用次数: 0

摘要

用伴结和模式结的对合一致不变量证明了绳结对合一致不变量的一个公式。因此，我们证明了只要结的对合一致性不变量中的任何一个是非零的，参数为（奇数，1）的结的任何迭代索都不是光滑切片。我们的公式也给出了绳结解结数的新边界，有时比其他已知的结花同源性的边界更强。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

A note on cables and the involutive concordance invariants

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A note on cables and the involutive concordance invariants

We prove a formula for the involutive concordance invariants of the cabled knots in terms of those of the companion knot and the pattern knot. As a consequence, we show that any iterated cable of a knot with parameters of the form (odd,1) is not smoothly slice as long as either of the involutive concordance invariants of the knot is nonzero. Our formula also gives new bounds for the unknotting number of a cabled knot, which are sometimes stronger than other known bounds coming from knot Floer homology.

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