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arXiv · 1211.2726

Quadruple crossing number of knots and links

Colin Adams
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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. 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.

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Colin Adams. 2013-01-28. Quadruple crossing number of knots and links. https://doi.org/10.1017/s0305004113000649

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