Braid index and Ropelength of alternating knots

Abstract: A long standing conjecture states that the ropelength of any alternating link is at least proportional to its crossing number. That is, there exists a constant $b_0>0$ such that $R(K)\ge b_0Cr(K)$ for any alternating link $K$, where $R(K)$ is the ropelength of $K$ and $Cr(K)$ is the crossing number of $K$. This conjecture has been recently proved affirmatively for the case of alternating knots. In this talk I will present the main results/ideas leading to the proof of this result, where the braid index served as the key bridge between the minimum crossing number and the ropelength of the knot.

geometric topology

Audience: researchers in the topic

GEOTOP-A seminar

Series comments: Web-seminar series on Applications of Geometry and Topology