The conjugacy problem for the group of any tame alternating knot is solvable
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- by K. I. Appel and P. E. Schupp PDF
- Proc. Amer. Math. Soc. 33 (1972), 329-336 Request permission
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
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K. I. Appel, The conjugacy problem for tame alternating knot groups is solvable, Notices Amer. Math. Soc. 18 (1971), 942. Abstract #71T-A227.
- Roger C. Lyndon, On Dehn’s algorithm, Math. Ann. 166 (1966), 208–228. MR 214650, DOI 10.1007/BF01361168 K. Reidemeister, Knotentheorie, Ergebnisse der Mathematik, Vol. 1, no. 1, Springer, Berlin, 1932.
- Horst Schubert, Die eindeutige Zerlegbarkeit eines Knotens in Primknoten, S.-B. Heidelberger Akad. Wiss. Math.-Nat. Kl. 1949 (1949), no. 3, 57–104 (German). MR 0031733
- Paul E. Schupp, On Dehn’s algorithm and the conjugacy problem, Math. Ann. 178 (1968), 119–130. MR 237620, DOI 10.1007/BF01350654
- C. M. 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 279169, DOI 10.1090/S0002-9939-1971-0279169-X
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 33 (1972), 329-336
- MSC: Primary 20F10
- DOI: https://doi.org/10.1090/S0002-9939-1972-0294460-X
- MathSciNet review: 0294460