On the conjugacy problem for knot groups

Abstract

A method is developed to show word and conjugacy problems solvable for a large class of knot groups.The class includes groups of a large number of non-alternating knots for which no previous conjugacy results have been obtained. The method involves a modification of the small cancellation diagrams ofLyndon and Schupp applied to Wirtinger presentations of knot groups.The crucial tool is a dual to each small cancellation diagram consisting of a set of curves in the plane of a projection of the knot.It is hoped that this approach will enable one to show that all knot groups have solvable eonjugacy problem.