Abstract

AbstractTwisting a knot in along a disjoint unknot produces a twist family of knots indexed by the integers. We prove that if the ratio of the Seifert genus to the slice genus for knots in a twist family limits to 1, then the winding number of about equals either zero or the wrapping number. As a key application, if or the mirror twist family contains infinitely many tight fibered knots, then the latter must occur. This leads to the characterization that is a braid axis of if and only if both and each contain infinitely many tight fibered knots. We also give a necessary and sufficient condition for to contain infinitely many L‐space knots, and apply the characterization to prove that satellite L‐space knots have braided patterns, which answers a question of both Baker–Moore and Hom in the positive. This result also implies an absence of essential Conway spheres for satellite L‐space knots, which gives a partial answer to a conjecture of Lidman–Moore.

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