Braid closure union braid axis is ribbon concordance minimal

Benjamin Daniels

geometric topology

Braid closure union braid axis is ribbon concordance minimal

arXiv:2607.14030

summary

The paper proves that a ribbon‑concordance‑minimal fibered knot in the 3‑sphere can produce ribbon‑concordance‑minimal links by attaching any braid closure in its complement, and that any link can be made ribbon‑concordance‑minimal by adding a single linked unknot.

Abstract

We show that a ribbon concordance minimal fibered knot $K$ in $S^{3}$ can generate ribbon concordance minimal links by the addition of any braid closure in $S^{3} ∖ K$ . As a corollary, we show that any link $L$ in $S^{3}$ may be made ribbon concordance minimal by adding a single unknot linked with $L$ . Our proofs use link Floer homology together with classical techniques.

7 pages, comments welcome!

Topics & keywords

#ribbon concordance #fibered knots #braid closures #link Floer homology #minimal linksribbon concordance minimalfibered knotbraid closurelink Floer homologyunknot additionS^3