On the conjugacy problem for knot groups

  • K. I. Appel
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 319)


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 of Lyndon 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 conjugacy problem.

Copyright information

© Springer Verlag 1973

Authors and Affiliations

  • K. I. Appel

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