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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© 1973 Springer Verlag
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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
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-06205-9
Online ISBN: 978-3-540-38479-3
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