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The word and conjugacy problems for the knot group of any tame, prime, alternating knot


Author: C. M. Weinbaum
Journal: Proc. Amer. Math. Soc. 30 (1971), 22-26
MSC: Primary 20.10; Secondary 55.00
DOI: https://doi.org/10.1090/S0002-9939-1971-0279169-X
MathSciNet review: 0279169
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Abstract: The decision problems in the title are solved using the solutions of the word and conjugacy problems obtained by Lyndon and Schupp, respectively, for certain classes of groups.


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

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  • [3] M. Dehn, Über die Topologie des drei-dimensionalen Raumes, Math. Ann. 69 (1910), 137-168. MR 1511580
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  • [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] F. Waldhausen, The word problem in fundamental groups of sufficiently large irreducible 3-manifolds, Ann. of Math. (2) 88 (1968), 272-280. MR 30 #2167. MR 0240822 (39:2167)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0279169-X
Keywords: Generators and relations, word problem, conjugacy problem, fundamental group, knot group, knot-diagram, tame knot, prime knot, alternating knot
Article copyright: © Copyright 1971 American Mathematical Society

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