English

A note on cables and the involutive concordance invariants

Geometric Topology 2025-06-05 v2

Abstract

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.

Keywords

Cite

@article{arxiv.2409.02192,
  title  = {A note on cables and the involutive concordance invariants},
  author = {Kristen Hendricks and Abhishek Mallick},
  journal= {arXiv preprint arXiv:2409.02192},
  year   = {2025}
}

Comments

Ten pages, one figure. To appear in the Bulletin of the LMS