Quadruple crossing number of knots and links-Reference-Cited by-同舟云学术

Quadruple crossing number of knots and links

Published:2013-11-20 Issue:2 Volume:156 Page:241-253
ISSN:0305-0041
Container-title:Mathematical Proceedings of the Cambridge Philosophical Society
language:en
Short-container-title:Math. Proc. Camb. Phil. Soc.

Author:

ADAMS COLIN

Abstract

AbstractA 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.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference10 articles.

1. C. Adams , O. Capovilla–Searle , J. Freeman , D. Irvine , S. Petti , D. Vitek , A. Weber and S. Zhang Bounds on Übercrossing and petal numbers for knots, in preparation 2013.

2. C. Adams , T. Crawford , B. DeMeo , M. Landry , A. Lin , M. Montee , S. Park , S. Venkatesh and F. Yhee Knot projections with a single multi-crossing. ArXiv:1208.5742 2012.

3. Jones polynomials of alternating links

4. C. Adams , O. Capovilla–Searle , J. Freeman , D. Irvine , S. Petti , D. Vitek , A. Weber and S. Zhang Multicrossing numbers and the span of the bracket polynomial, ArXiv 1311.0526 2013.

5. Degenerate Crossing Numbers

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