Geometrically and diagrammatically maximal knots
Geometric Topology
2018-11-16 v4
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.
Keywords
Cite
@article{arxiv.1411.7915,
title = {Geometrically and diagrammatically maximal knots},
author = {Abhijit Champanerkar and Ilya Kofman and Jessica S. Purcell},
journal= {arXiv preprint arXiv:1411.7915},
year = {2018}
}
Comments
26 pages, 12 figures. V2: Updated references, removed hypothesis from Theorem 1.4, added Corollary 1.11, and made other minor wording changes. V3: Discussion on weaving knots has been moved into another paper. V4: Added Figures 10 and 12, minor wording changes