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STICK INDEX OF KNOTS AND LINKS IN THE CUBIC LATTICE

COLIN ADAMS

Department of Mathematics and Statistics, Williams College, Williamstown, MA 01267, USA

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MICHELLE CHU

Department of Mathematics, University of Texas, 1 University Station, C1200 Austin, TX 78712, USA

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THOMAS CRAWFORD

Department of Mathematics and Statistics, Williams College, Williamstown, MA 01267, USA

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STEPHANIE JENSEN

Department of Mathematics and Statistics, Williams College, Williamstown, MA 01267, USA

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KYLER SIEGEL

Department of Mathematics, Stanford University, Building 380, Stanford, CA 943057, USA

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, and

LIYANG ZHANG

Department of Mathematics and Statistics, Williams College, Williamstown, MA 01267, USA

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https://doi.org/10.1142/S0218216511009935Cited by:13 (Source: Crossref)

Abstract

The cubic lattice stick index of a knot type is the least number of sticks glued end-to-end that are necessary to construct the knot type in the 3-dimensional cubic lattice. We present the cubic lattice stick index of various knots and links, including all (p, p + 1)-torus knots, and show how composing and taking satellites can be used to obtain the cubic lattice stick index for a relatively large infinite class of knots. Additionally, we present several bounds relating cubic lattice stick index to other known invariants.

Keywords:

AMSC: 57M25, 57M27

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