Satellite fully positive braid links are braided satellite of fully positive braid links
Abstract
A link in S3 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.
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