Parabolic Representations of the Groups of Mutant Knots

Abstract

It is proved that the groups of the Kinoshita-Terasaka knot and the Conway's knot have the same number of parabolic representations in SL2(F) for every finite field F. Although the proof is based on the fact that the two knots are mutants of each other, it is also shown that the groups of mutant knots do not in general have the same number of parabolic representations.