Symmetric Criticality for Ropelength
Seminar Room 1, Newton Institute
The ropelength of a link embedded in $R^3$ is the ratio of the curve's length to its thickness. Jason Cantarella, Joe Fu, Rob Kusner, and John Sullivan have developed a theory of first order criticality for ropelength. We will discuss an extension of this work for the case of link conformations with rigid rotational symmetry. As an application we will prove that there is an infinite class of knots for which there are geometrically distinct ropelength critical conformations. This work is joint with Jason Cantarella, Jennifer Ellis, and Joe Fu.