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A new bridge index for links with trivial knot components

Published online by Cambridge University Press:  01 October 2012

YORIKO KODANI
YORIKO KODANI*
Affiliation:
Department of Mathematics, Nara Women's University, Kitauoya Nishimachi, Nara 630-8506, Japan. e-mail: [email protected]
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Abstract

Let L = K1 ∪ K2 be a 2-component link in the 3-sphere such that K1 is a trivial knot. In this paper, we introduce a new bridge index, denoted by bK1 = 1([L]), for L. Roughly speaking, bK1 = 1([L]) is the minimum of the bridge numbers of the links ambient isotopic to L under the constraint that all of the bridge numbers of the components corresponding to K1 are 1. We provide a lower bound estimate of bK1 = 1([L]) in the case when L is a non-split satellite link. By using this result, we show that for each integer n(≥ 2), there exists a link Ln = K1n ∪ K2n with K1n a trivial knot such that bK1n = 1([Ln])−b([Ln]) = n−1, where b([Ln]) is the bridge index of Ln.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 154 , Issue 2 , March 2013 , pp. 279 - 286
Copyright
Copyright © Cambridge Philosophical Society 2012

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References

REFERENCES

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