Torsion in the knot concordance group and cabling

Sungkyung Kang; JungHwan Park

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arXiv · 2207.11870

Torsion in the knot concordance group and cabling

Sungkyung Kang·JungHwan Park

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Abstract

We define a nontrivial mod 2 valued additive concordance invariant defined on the torsion subgroup of the knot concordance group using involutive knot Floer package. For knots not contained in its kernel, we prove that their iterated $(\text{odd},1)$-cables have infinite order in the concordance group and, among them, infinitely many are linearly independent. Furthermore, by taking $(2,1)$-cables of the aforementioned knots, we present an infinite family of knots which are strongly rationally slice but not slice.

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Sungkyung Kang, JungHwan Park. 2022-07-25. Torsion in the knot concordance group and cabling. https://arxiv.org/abs/2207.11870

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