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Genus one 1-bridge positions for the trivial knot and cabled knots

Published online by Cambridge University Press:  01 January 1999

CHUICHIRO HAYASHI
CHUICHIRO HAYASHI
Affiliation:
Department of Mathematics, Faculty of Science, Gakushuin University, Mejiro 1-5-1, Toshima-ku, Tokyo 171, Japan; e-mail: Chuichiro.Hayashi@gakushuin.ac.jp
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Abstract

Let (Vi, ti) be a pair consisting of a solid torus Vi and an unknotted arc ti properly imbedded in Vi for i=1 and 2. Taking the union of these pairs we obtain a pair (M, K) of the 3-dimensional sphere or a lens space M and a knot K. We call such a knot K a genus one 1-bridge knot. In this paper we determine when a genus one 1-bridge knot is the trivial knot or a cabled knot.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 125 , Issue 1 , January 1999 , pp. 53 - 65
Copyright
Cambridge Philosophical Society 1999

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