Gordian Adjacency for Positive Braid Knots
Abstract
A knot K1 is said to be Gordian adjacent to a knot K2 if K1 is an intermediate knot on an unknotting sequence of K2. We extend previous results on Gordian adjacency by showing sufficient conditions for Gordian adjacency between classes of positive braid knots through manipulations of braid words. In addition, we explore unknotting sequences of positive braid knots and give a proof that there are only finitely many positive braid knots for a given unknotting number.
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