Additivity of Bridge Number of Knots

Jennifer Schultens

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Additivity of Bridge Number of Knots

Jennifer Schultens

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Abstract

We provide a new proof of the following results of H. Schubert: If K is a satellite knot with companion J and pattern L that lies in a solid torus T in which it has index k, then the bridge numbers satisfy the following: 1) The bridge number of K is greater than or equal to the product of k and the bridge number of J; 2) If K is a composite knot (this is the case k = 1), then the bridge number of K is one less than the sum of the bridge numbers of J and L.

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BibTeX RIS

Jennifer Schultens. 2001-11-02. Additivity of Bridge Number of Knots. https://arxiv.org/abs/math/0111032

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