A knot $K_1$ is said to be Gordian adjacent to a knot $K_2$ if $K_1$ is an intermediate knot on an unknotting sequence of $K_2$. 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.

Author Bio

Tolson H. Bell: Tolson Bell is a mathematics major at Georgia Institute of Technology with a concentration in discrete mathematics and a minor in artificial intelligence. When not solving math problems, he enjoys cross country running.

David C. Luo: David Luo is a fourth-year undergraduate student at Emory University majoring in mathematics and minoring in computer science. In his free time, he enjoys playing basketball with friends and trying new restaurants. Following college, he plans to pursue a PhD in mathematics.

Luke Seaton: Luke Seaton is a senior mathematics major at Louisiana Tech University. In addition to math, he is passionate about exploring the world and transgender advocacy. Luke plans to pursue a PhD in mathematics.

Samuel P. Serra: Sam Serra is a third-year mathematics major at University of Colorado Boulder. After graduation, Sam plans to pursue graduate study in mathematics. In his free time, he can be found singing in choir and hiking in the Rocky mountains.