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Quadruple crossing number of knots and links

Published online by Cambridge University Press:  20 November 2013

COLIN ADAMS
COLIN ADAMS*
Affiliation:
Department of Mathematics and Statistics, Williams College, Williamstown, MA 01267, U.S.A. e-mail: Colin.C.Adams@williams.edu
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Abstract

A quadruple crossing is a crossing in a projection of a knot or link that has four strands of the knot passing straight through it. A quadruple crossing projection is a projection such that all of the crossings are quadruple crossings. In a previous paper, it was proved that every knot and link has a quadruple crossing projection and hence, every knot has a minimal quadruple crossing number c4(K). In this paper, we investigate quadruple crossing number, and in particular, use the span of the bracket polynomial to determine quadruple crossing number for a variety of knots and links.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 156 , Issue 2 , March 2014 , pp. 241 - 253
Copyright
Copyright © Cambridge Philosophical Society 2013 

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References

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