An infinite family of Legendrian torus knots distinguished by cube number

Ben McCarty

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arXiv · 1012.4482

An infinite family of Legendrian torus knots distinguished by cube number

Ben McCarty

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Abstract

For a knot $K$ the cube number is a knot invariant defined to be the smallest $n$ for which there is a cube diagram of size $n$ for $K$. There is also a Legendrian version of this invariant called the \emph{Legendrian cube number}. We will show that the Legendrian cube number distinguishes the Legendrian left hand torus knots with maximal Thurston-Bennequin number and maximal rotation number from the Legendrian left hand torus knots with maximal Thurston-Bennequin number and minimal rotation number.

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Ben McCarty. 2010-12-20. An infinite family of Legendrian torus knots distinguished by cube number. https://arxiv.org/abs/1012.4482

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