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arXiv · 2610.31654

On the Concordance Invariants of Cable Links

Aadhishwaran Bhuvaraghamoorthy
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Abstract

We study the Beliakova--Wehrli link $s$-invariant and Cavallo's link $τ$-invariant of coherently oriented cables. For knots satisfying extremal four-ball genus and maximal self-linking hypotheses, we establish bounds for the $s$-invariant of $(p,q)$-cables, where $p$ and $q$ are not necessarily coprime, and show that these bounds are sharp under certain conditions. For the $τ$-invariant, we prove analogous bounds for arbitrary companion knots and exact formulas whenever $τ(K)=\pm g_4(K)\ne 0$. Specializing to the coherently oriented cable links associated to an $n$-framed knot, we apply these bounds to the lasagna $s$-invariant of Ren and Willis. The resulting applications provide upper bounds for the lasagna $s$-invariant of knot traces and a criterion for distinguishing homeomorphic zero traces up to orientation-preserving diffeomorphism.

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Aadhishwaran Bhuvaraghamoorthy. 2026-10-22. On the Concordance Invariants of Cable Links. https://arxiv.org/abs/2610.31654

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