Geometrically and diagrammatically maximal knots

نویسندگان

  • Abhijit Champanerkar
  • Ilya Kofman
  • Jessica S. Purcell
چکیده

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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عنوان ژورنال:
  • J. London Math. Society

دوره 94  شماره 

صفحات  -

تاریخ انتشار 2016