Symmetric Criticality for Tight Knots

Abstract

We prove a version of symmetric criticality for ropelength-critical knots. Our theorem implies that a knot or link with a symmetric representative has a ropelength-critical configuration with the same symmetry. We use this to construct new examples of ropelength critical configurations for knots and links which are different from the ropelength minima for these knot and link types.Comment: This version adds references, and most importantly an acknowledgements section which should have been in the original postin