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On the conjugacy problem for knot groups

On the conjugacy problem for knot groups

  • K. I. Appel 
  • Conference paper
  • First Online: 01 January 2006
  • 2007 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 319)

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 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.

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  1. K. I. Appel
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    © 1973 Springer Verlag

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    Cite this paper

    Appel, K.I. (1973). On the conjugacy problem for knot groups. In: Gatterdam, R.W., Weston, K.W. (eds) Conference on Group Theory. Lecture Notes in Mathematics, vol 319. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0058925

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    • DOI: https://doi.org/10.1007/BFb0058925

    • Published: 18 August 2006

    • Publisher Name: Springer, Berlin, Heidelberg

    • Print ISBN: 978-3-540-06205-9

    • Online ISBN: 978-3-540-38479-3

    • eBook Packages: Springer Book Archive

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