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Examples of tunnel number one knots which have the property ‘1 + 1 = 3’

Published online by Cambridge University Press:  24 October 2008

Kanji Morimoto ,
Makoto Sakuma  and
Yoshiyuki Yokota
Kanji Morimoto
Affiliation:
Department of Mathematics, Takushoku University, Tatemachi, Hachioji, Tokyo 193, Japan
Makoto Sakuma
Affiliation:
Department of Mathematics, Faculty of Science. Osaka University, Machikaneyama-cho 1-16, Toyonaka, Osaka 560, Japan
Yoshiyuki Yokota
Affiliation:
Graduate School of Mathematics, Kyushu University, Fukuoka 812, Japan
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Extract

Let K be a knot in the 3-sphere S3, N(K) the regular neighbourhood of K and E(K) = cl(S3−N(K)) the exterior of K. The tunnel number t(K) is the minimum number of mutually disjoint arcs properly embedded in E(K) such that the complementary space of a regular neighbourhood of the arcs is a handlebody. We call the family of arcs satisfying this condition an unknotting tunnel system for K. In particular, we call it an unknotting tunnel if the system consists of a single arc.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 119 , Issue 1 , January 1996 , pp. 113 - 118
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

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