关于电缆和渐开线协变的说明

arXiv - MATH - Geometric Topology Pub Date : 2024-09-03 DOI:arxiv-2409.02192

Kristen Hendricks, Abhishek Mallick

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引用次数: 0

摘要

我们根据伴结和模式结的无关协整不变量证明了索结的无关协整不变量公式。因此，我们证明了只要绳结的任一渐开线协整不变式不为零，参数为（奇，1）形式的绳结的任何迭代绳结都不是平滑切分的。我们的公式还给出了缆索结的解结数的新边界，它有时比来自结浮子同源性的其他已知边界更强。

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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 that 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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arXiv - MATH - Geometric Topology

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