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Additivity of bridge numbers of knots

Published online by Cambridge University Press:  24 October 2003

JENNIFER SCHULTENS
JENNIFER SCHULTENS
Affiliation:
Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, U.S.A. e-mail: [email protected]
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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 $(\skew1\hat{V}, L)$ with index $k$, then the bridge numbers satisfy the following: $b(K) \geq k \cdot (b(J))$. In addition, if $K$ is a composite knot with summands $J$ and $L$, then $b(K) = b(J) + b(L) - 1.$

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 135 , Issue 3 , November 2003 , pp. 539 - 544
Copyright
© 2003 Cambridge Philosophical Society

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