On the Concordance Invariants of Cable Links
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)=± g4(K)≠ 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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BibTeX
@misc{bhuvaraghamoorthy2026concordance,
title = {{On the Concordance Invariants of Cable Links}},
author = {Aadhishwaran Bhuvaraghamoorthy},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31654},
eprint = {2610.31654},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31654},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the Concordance Invariants of Cable Links
AU - Aadhishwaran Bhuvaraghamoorthy
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31654
UR - https://arxiv.org/abs/2610.31654
AB - 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)=± g_4(K)≠ 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.
ER -