Volume bounds for weaving knots

Abhijit Champanerkar; Ilya Kofman; Jessica Purcell

doi:10.2140/agt.2016.16.3301

Volume bounds for weaving knots

Abhijit Champanerkar, Ilya Kofman, Jessica Purcell

School of Mathematics

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

12 Citations (Scopus)

Abstract

Weaving knots are alternating knots with the same projection as torus knots, and were conjectured by X-S Lin to be among the maximum volume knots for fixed crossing number. We provide the first asymptotically sharp volume bounds for weaving knots, and we prove that the infinite square weave is their geometric limit.

Original language	English
Pages (from-to)	3301-3323
Number of pages	23
Journal	Algebraic and Geometric Topology
Volume	16
Issue number	6
DOIs	https://doi.org/10.2140/agt.2016.16.3301
Publication status	Published - 15 Dec 2016

Keywords

hyperbolic volume
weaving knot
crossing number
geometric limit

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10.2140/agt.2016.16.3301

Cite this

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title = "Volume bounds for weaving knots",

abstract = "Weaving knots are alternating knots with the same projection as torus knots, and were conjectured by X-S Lin to be among the maximum volume knots for fixed crossing number. We provide the first asymptotically sharp volume bounds for weaving knots, and we prove that the infinite square weave is their geometric limit.",

keywords = "hyperbolic volume, weaving knot, crossing number, geometric limit",

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

year = "2016",

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doi = "10.2140/agt.2016.16.3301",

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AU - Champanerkar, Abhijit

AU - Kofman, Ilya

AU - Purcell, Jessica

PY - 2016/12/15

Y1 - 2016/12/15

N2 - Weaving knots are alternating knots with the same projection as torus knots, and were conjectured by X-S Lin to be among the maximum volume knots for fixed crossing number. We provide the first asymptotically sharp volume bounds for weaving knots, and we prove that the infinite square weave is their geometric limit.

AB - Weaving knots are alternating knots with the same projection as torus knots, and were conjectured by X-S Lin to be among the maximum volume knots for fixed crossing number. We provide the first asymptotically sharp volume bounds for weaving knots, and we prove that the infinite square weave is their geometric limit.

KW - hyperbolic volume

KW - weaving knot

KW - crossing number

KW - geometric limit

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DO - 10.2140/agt.2016.16.3301

M3 - Article

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EP - 3323

JO - Algebraic and Geometric Topology

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SN - 1472-2747

IS - 6

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Volume bounds for weaving knots

Abstract

Keywords

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Other files and links

Quantum invariants and hyperbolic manifolds in three-dimensional topology

Cite this

Volume bounds for weaving knots

Abstract

Keywords

Access to Document

Other files and links

Projects

Quantum invariants and hyperbolic manifolds in three-dimensional topology

Cite this