The word and conjugacy problems for the knot group of any tame, prime, alternating knot
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- by C. M. Weinbaum PDF
- Proc. Amer. Math. Soc. 30 (1971), 22-26 Request permission
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
- J. W. Alexander, Topological invariants of knots and links, Trans. Amer. Math. Soc. 30 (1928), no. 2, 275–306. MR 1501429, DOI 10.1090/S0002-9947-1928-1501429-1
- Richard H. Crowell and Ralph H. Fox, Introduction to knot theory, Ginn and Company, Boston, Mass., 1963. Based upon lectures given at Haverford College under the Philips Lecture Program. MR 0146828
- M. Dehn, Über die Topologie des dreidimensionalen Raumes, Math. Ann. 69 (1910), no. 1, 137–168 (German). MR 1511580, DOI 10.1007/BF01455155
- Roger C. Lyndon, On Dehn’s algorithm, Math. Ann. 166 (1966), 208–228. MR 214650, DOI 10.1007/BF01361168
- Paul E. Schupp, On Dehn’s algorithm and the conjugacy problem, Math. Ann. 178 (1968), 119–130. MR 237620, DOI 10.1007/BF01350654
- Friedhelm Waldhausen, The word problem in fundamental groups of sufficiently large irreducible $3$-manifolds, Ann. of Math. (2) 88 (1968), 272–280. MR 240822, DOI 10.2307/1970574
Additional Information
- © Copyright 1971 American Mathematical Society
- 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