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On the braid index of links with nested diagrams

Published online by Cambridge University Press:  24 October 2008

D. A. Chalcraft
D. A. Chalcraft
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, Cambridge CB2 1SB
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Abstract

The number of Seifert circuits in a diagram of a link is well known 9 to be an upper bound for the braid index of the link. The -breadth of the so-called P-polynomial 3 of the link is known 5, 2 to give a lower bound. In this paper we consider a large class of links diagrams, including all diagrams where the interior of every Seifert circuit is empty. We show that either these bounds coincide, or else the upper bound is not sharp, and we obtain a very simple criterion for distinguishing these cases.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 111 , Issue 2 , March 1992 , pp. 273 - 281
Copyright
Copyright © Cambridge Philosophical Society 1992

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References

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