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Some links with non-adequate minimal-crossing diagrams

Published online by Cambridge University Press:  24 October 2008

Masao Hara  and
Makoto Yamamoto
Masao Hara
Affiliation:
Department of Mathematics, School of Education, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku, Tokyo 16950, Japan
Makoto Yamamoto
Affiliation:
Department of Applied Mathematics, Osaka Women's University, 2-1, Daisen-cho, Sakai, Osaka 590, Japan
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Extract

To investigate invariants of links derived from their diagrams, the recent new polynomial invariants of links play important roles. Murasugi6, 7, Kauffman3 and Thistlethwaite 9 independently showed that the number of crossings in a proper connected alternating diagram of a link is the minimal-crossing number of the link and that the writhe of the diagram is invariant. Murasugi 8 also determined the minimal-crossing number of torus links. In 5, Lickorish and Thistlethwaite introduced the concept of an adequate link diagram and showed that the number of crossings in an adequate diagram of a semi-alternating link is the minimal-crossing number of the link. They also determined the minimal-crossing number of almost all Montesinos links. In this paper we show that for some links represented by plats and braids which are not adequate, the numbers of crossings in the diagrams are the minimal-crossing numbers of the links.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 111 , Issue 2 , March 1992 , pp. 283 - 289
Copyright
Copyright © Cambridge Philosophical Society 1992

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References

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