Satellite fully positive braid links are braided satellite of fully positive braid links

Abstract

A link in $S^3$ is a fully positive braid link if it is the closure of a positive braid that contains at least one full-twist. We show that a fully positive braid link is a satellite link if and only if it is the satellite of a fully positive braid link $C$ such that the pattern is a positive braid that contains sufficiently many full twists, where the number of necessary full twists only depends on $C$. As an application, we give a characterization of the unknot by the property that certain braided satellite is a (fully) positive braid knot.

15 pages, 3 figures. v3, inaccurate descriptions of super summit sets are corrected

Cited by in corpus (1)

• The second coefficient of the Alexander polynomial as a satellite obstruction