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The conjugacy problem for the group of any tame alternating knot is solvable. (English) Zbl 0243.20036

MSC:
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
20F05 Generators, relations, and presentations of groups
20F34 Fundamental groups and their automorphisms (group-theoretic aspects)
57M05 Fundamental group, presentations, free differential calculus
57M25 Knots and links in the \(3\)-sphere (MSC2010)
03D40 Word problems, etc. in computability and recursion theory
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[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] Roger C. Lyndon, On Dehn’s algorithm, Math. Ann. 166 (1966), 208 – 228. · Zbl 0138.25702 · doi:10.1007/BF01361168 · doi.org
[3] K. Reidemeister, Knotentheorie, Ergebnisse der Mathematik, Vol. 1, no. 1, Springer, Berlin, 1932. · JFM 58.1202.04
[4] Horst Schubert, Die eindeutige Zerlegbarkeit eines Knotens in Primknoten, S.-B. Heidelberger Akad. Wiss. Math.-Nat. Kl. 1949 (1949), no. 3, 57 – 104 (German). · Zbl 0031.28602
[5] Paul E. Schupp, On Dehn’s algorithm and the conjugacy problem, Math. Ann. 178 (1968), 119 – 130. · Zbl 0164.01901 · doi:10.1007/BF01350654 · doi.org
[6] 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. · Zbl 0228.55004
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