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Satellite fully positive braid links are braided satellite of fully positive braid links
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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.
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Cited by 1 Pith paper
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Hyperbolic knots with arbitrarily large torsion order in knot Floer homology
The twisted torus knots T(p,kp+1;2,1) are hyperbolic for p >= 5 and realize arbitrarily large values of both torsion orders Ord and Ord'.
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