Geometrically and diagrammatically maximal knots

  title={Geometrically and diagrammatically maximal knots},
  author={Abhijit Champanerkar and Ilya Kofman and Jessica S. Purcell},
  journal={J. London Math. Society},
The ratio of volume to crossing number of a hyperbolic knot is known to be bounded above by the volume of a regular ideal octahedron, and a similar bound is conjectured for the knot determinant per crossing. We investigate a natural question motivated by these bounds: For which knots are these ratios nearly maximal? We show that many families of alternating knots and links simultaneously maximize both ratios. 


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