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The conjugacy problem for the group of any tame alternating knot is solvable

Authors: K. I. Appel and P. E. Schupp
Journal: Proc. Amer. Math. Soc. 33 (1972), 329-336
MSC: Primary 20F10
MathSciNet review: 0294460
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Abstract: The theorem of the title is proved by using the techniques of Weinbaum along with the prime decomposition of knots and an extension of some small cancellation techniques of Lyndon and Schupp.

References [Enhancements On Off] (What's this?)

  • [1] K. I. Appel, The conjugacy problem for tame alternating knot groups is solvable, Notices Amer. Math. Soc. 18 (1971), 942. Abstract #71T-A227.
  • [2] R. C. Lyndon, On Dehn's algorithm, Math. Ann. 166 (1966), 208-226. MR 35 #5499. MR 0214650 (35:5499)
  • [3] K. Reidemeister, Knotentheorie, Ergebnisse der Mathematik, Vol. 1, no. 1, Springer, Berlin, 1932.
  • [4] H. Schubert, Der eindeutige Zerlegbarkeit eines Knotens in Primknoten, S.-B. Heidelberger Akad. Wiss. Math.-Nat. Kl. 1949, no. 3, 57-104. MR 11, 196. MR 0031733 (11:196f)
  • [5] P. E. Schupp, On Dehn's algorithm and the conjugacy problem, Math. Ann. 178 (1968), 119-130. MR 38 #5901. MR 0237620 (38:5901)
  • [6] C. Weinbaum, The word and conjugacy problems for the knot group of any tame prime alternating knot, Proc. Amer. Math. Soc. 30 (1971), 22-26. MR 0279169 (43:4895)

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Keywords: Conjugacy problem, word problem, fundamental group, knot group, knot diagram, tame knot, prime knot, alternating knot, generators, relations
Article copyright: © Copyright 1972 American Mathematical Society

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