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Links with super-additive tunnel number

Published online by Cambridge University Press:  24 October 2008

Michel Boileau ,
Martin Lustig  and
Yoav Moriah
Michel Boileau
Affiliation:
Université Paul Sabatier, Département de Mathématiques, 118 route de Narbonne, 31062 Toulouse, France
Martin Lustig
Affiliation:
Institut für Mathematik, Ruhr-Universität Bochum, Postfach 10 21 48, 4630 Bochum 1, Germany
Yoav Moriah
Affiliation:
Department of Mathematics, Technion, Haifa 32000, Israel
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Extract

Let L ⊂ S3 be a knot or a link. A tunnel system for L is a collection of disjoint arcs t1, … ts properly embedded in S3−N(L) so that is a handlebody. Alternatively one can view the t1, … ts ascocores of 2-handles which have to be attached to a handlebody in order to obtain S3−N(L). It follows immediately that this handlebody is of genus s+1. The tunnel number of L, denoted by t(L), is defined to be the minimal cardinality of all such collections.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 115 , Issue 1 , January 1994 , pp. 85 - 95
Copyright
Copyright © Cambridge Philosophical Society 1994

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References

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