Nonalgebraic killers of knot groups
Author:
Chichen M. Tsau
Journal:
Proc. Amer. Math. Soc. 95 (1985), 139-146
MSC:
Primary 57M05; Secondary 57M25
DOI:
https://doi.org/10.1090/S0002-9939-1985-0796463-4
MathSciNet review:
796463
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Abstract | References | Similar Articles | Additional Information
Abstract: We show that a knot exists with the property that there exists a killer of the knot group which is not the image of the meridian under any automorphism.
- [1] R. H. Bing and J. M. Martin, Cubes with knotted holes, Trans. Amer. Math. Soc. 155 (1971), 217–231. MR 0278287, https://doi.org/10.1090/S0002-9947-1971-0278287-4
- [2] James W. Cannon and C. D. Feustel, Essential embeddings of annuli and Möbius bands in 3-manifolds, Trans. Amer. Math. Soc. 215 (1976), 219–239. MR 0391094, https://doi.org/10.1090/S0002-9947-1976-0391094-1
- [3] Klaus Johannson, Homotopy equivalences of 3-manifolds with boundaries, Lecture Notes in Mathematics, vol. 761, Springer, Berlin, 1979. MR 551744
- [4] Horst Schubert, Knoten und Vollringe, Acta Math. 90 (1953), 131–286 (German). MR 0072482, https://doi.org/10.1007/BF02392437
- [5] Peter B. Shalen, Infinitely divisible elements in 3-manifold groups, Knots, groups, and 3-manifolds (Papers dedicated to the memory of R. H. Fox), Princeton Univ. Press, Princeton, N.J., 1975, pp. 293–335. Ann. of Math. Studies, No. 84. MR 0375280
- [6] C. Tsau, Killers of knot groups, Ph. D. Thesis, University of Iowa, 1983.
-manifolds, Trans. Amer. Math. Soc. 215 (1976), 219-239. 
-manifolds with boundaries, Lecture Notes in Math., vol. 761, Springer-Verlag, Berlin, Heidelberg, New York, 1979. 
-manifold groups, Ann. of Math. Studies, No. 84, Princeton Univ. Press, Princeton, N. J., 1975. Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57M05, 57M25
Retrieve articles in all journals with MSC: 57M05, 57M25
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1985-0796463-4
Keywords:
Knot manifold,
knot group,
presentation,
automorphism of knot group,
satellite knot,
winding number,
wrapping number,
incompressible surface,
essential map of annulus
Article copyright:
© Copyright 1985
American Mathematical Society
