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ON KILLERS OF CABLE KNOT GROUPS

Part of: Low-dimensional topology

Published online by Cambridge University Press:  06 February 2017

EDERSON R. F. DUTRA
EDERSON R. F. DUTRA*
Affiliation:
Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn Str. 4, 24098 Kiel, Germany email dutra@math.uni-kiel.de
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Abstract

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A killer of a group $G$ is an element that normally generates $G$. We show that the group of a cable knot contains infinitely many killers such that no two lie in the same automorphic orbit.

Keywords

knotkillercable knot group

MSC classification

Primary: 57M25: Knots and links in $S^3$
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 96 , Issue 1 , August 2017 , pp. 171 - 176
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

References

Aschenbrenner, M., Friedl, S. and Wilton, H., ‘3-manifold groups’, European Mathematical Society, Zurich, Switzerland, 2015. arXiv:1205.0202v3 [math.GT].Google Scholar
Jaco, W. and Shalen, P., ‘Seifert fibered spaces in 3-manifolds’, Mem. Amer. Math. Soc., 220 (Amer. Math. Soc., Providence, RI, 1979).Google Scholar
Johannson, K., Homotopy Equivalences of 3-Manifolds with Boundary, Lecture Notes in Mathematics, 761 (Springer, Berlin–New York, 1979).Google Scholar
Silver, D. S., Whitten, W. and Williams, S. G., ‘Knot groups with many killers’, Bull. Aust. Math. Soc. 81 (2010), 507–513.Google Scholar
Simon, J., ‘Wirtinger approximations and the knot groups of F n in S n+1 ’, Pacific J. Math. 90 (1990), 177–189.CrossRefGoogle Scholar
Tsau, C. M., ‘Nonalgebraic killers of knot groups’, Proc. Amer. Math. Soc. 95 (1985), 139–146.Google Scholar