Geometrically and diagrammatically maximal knots

Abhijit Champanerkar, Ilya Kofman, Jessica Purcell

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11 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)883-908
Number of pages26
JournalJournal of the London Mathematical Society
Volume94
Issue number3
DOIs
Publication statusPublished - 2016

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