Geometrically and diagrammatically maximal knots

Abhijit Champanerkar; Ilya Kofman; Jessica Purcell

doi:10.1112/jlms/jdw062

Geometrically and diagrammatically maximal knots

Abhijit Champanerkar, Ilya Kofman, Jessica Purcell

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

15 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 language	English
Pages (from-to)	883-908
Number of pages	26
Journal	Journal of the London Mathematical Society
Volume	94
Issue number	3
DOIs	https://doi.org/10.1112/jlms/jdw062
Publication status	Published - 2016

Access to Document

10.1112/jlms/jdw062

Cite this

@article{a3179bb10e6c43548725bbc0e6848c08,

title = "Geometrically and diagrammatically maximal knots",

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.",

author = "Abhijit Champanerkar and Ilya Kofman and Jessica Purcell",

year = "2016",

doi = "10.1112/jlms/jdw062",

language = "English",

volume = "94",

pages = "883--908",

journal = "Journal of the London Mathematical Society",

issn = "0024-6107",

publisher = "Wiley-Blackwell",

number = "3",

}

TY - JOUR

T1 - Geometrically and diagrammatically maximal knots

AU - Champanerkar, Abhijit

AU - Kofman, Ilya

AU - Purcell, Jessica

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85015066340&partnerID=8YFLogxK

U2 - 10.1112/jlms/jdw062

DO - 10.1112/jlms/jdw062

M3 - Article

AN - SCOPUS:85015066340

SN - 0024-6107

VL - 94

SP - 883

EP - 908

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

IS - 3

ER -

Geometrically and diagrammatically maximal knots

Abstract

Access to Document

Other files and links

Quantum invariants and hyperbolic manifolds in three-dimensional topology

Cite this

Geometrically and diagrammatically maximal knots

Abstract

Access to Document

Other files and links

Projects

Quantum invariants and hyperbolic manifolds in three-dimensional topology

Cite this