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Hypercube Diagrams For Knots, Links, And Knotted Tori, Ben Mccarty
Hypercube Diagrams For Knots, Links, And Knotted Tori, Ben Mccarty
LSU Doctoral Dissertations
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. Examples of knots for which the cube number detects chirality are presented. There is also a Legendrian version of this invariant called the 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. Finally, there is a generalization of cube …