The ropelength conjecture of alternating knots

Abstract

A long standing conjecture states that the ropelength of any alternating knot is at least proportional to its crossing number. In this paper we prove that this conjecture is true. That is, there exists a constant b0 > 0 such that R(K) ≥ b0Cr(K) for any alternating knot K, where R(K) is the ropelength of K and Cr(K) is the crossing number of K. In this paper, we prove that this conjecture is true and establish that b0 > 1/56.