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On the conjugacy problem for knot groups. (English) Zbl 0276.20033

MSC:
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
03D40 Word problems, etc. in computability and recursion theory
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)
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References:
[1] Appel, K.I.: The Conjugacy Problem for Tame Alternating Knot Groups Is Solvable, Abstract 71 TA 227, Notices Amer. math Soc.18 (1971)
[2] Appel, K. I., Schupp, P. E.: The Conjugacy Problem for the Group of any Tame Alternating Knot Is Solvable, Proc. Amer. math Soc.33, 329-336 (1972) · Zbl 0243.20036 · doi:10.1090/S0002-9939-1972-0294460-X
[3] Chinn, W. G., Steenrod, N. G.: First Concepts of Topology, New York: Random House 1966 · Zbl 0201.55303
[4] Crowell, R. H., Fox, R. H.: Introduction to Knot Theory, Boston, Ginn and Co. 1962
[5] Little, C. N.: Non-alternative?Knots, Trans. roy. Soc. Edinburgh39, 771-778 (with 3 plates) (1900) · JFM 31.0481.02
[6] Liu, C. L.: Introduction to Combinatorial Mathematics, New York: McGraw Hill 1968
[7] Lyndon, R. C.: On Dehn’s Algorithm, Math. Ann.166, 208-226 (1968) · Zbl 0138.25702 · doi:10.1007/BF01361168
[8] Reidemeister, K.: Knotentheorie, Berlin: Springer 1932
[9] Schubert, H.: Die eindeutige Zerlegbarkeit eines Knotens in Primknoten, S.-ber. Heidelberger Akad. Wiss., math. naturw. Kl.3, 57-104 (1949) · Zbl 0031.28602
[10] Schupp, P. E.: On Dehn’s Algorithm and the Conjugacy Problem, Math. Ann.178, 119-130 (1968) · Zbl 0164.01901 · doi:10.1007/BF01350654
[11] Waldhausen, F.: The Word Problem in Fundamental Groups of Sufficiently Large Irreducible 3-manifolds, Ann. of Math., II. Ser.88, 272-280 (1968) · Zbl 0167.52103 · doi:10.2307/1970574
[12] Weinbaum, C. M.: The Word and Conjugacy Problems for the Knot Group of any Tame Prime Alternating Knot, Proc. Amer. math. Soc.22, 267-269 (1971) · Zbl 0228.55004
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