Volumes of highly twisted knots and links

Jessica Purcell

doi:10.2140/agt.2007.7.93

Volumes of highly twisted knots and links

Jessica Purcell

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

23 Citations (Scopus)

Abstract

We show that for a large class of knots and links with complements in S 3 admitting a hyperbolic structure, we can determine bounds on the volume of the link complement from combinatorial information given by a link diagram. Specifically, there is a universal constant C such that if a knot or link admits a prime, twist reduced diagram with at least 2 twist regions and at least C crossings per twist region, then the link complement is hyperbolic with volume bounded below by 3.3515 times the number of twist regions in the diagram. C is at most 113.

Original language	English
Pages (from-to)	93-108
Number of pages	16
Journal	Algebraic and Geometric Topology
Volume	7
Issue number	1
DOIs	https://doi.org/10.2140/agt.2007.7.93
Publication status	Published - 1 Dec 2007
Externally published	Yes

Keywords

Cone manifolds
Hyperbolic knot complements
Hyperbolic link complements
Volume

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10.2140/agt.2007.7.93

Cite this

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KW - Hyperbolic knot complements

KW - Hyperbolic link complements

KW - Volume

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Volumes of highly twisted knots and links

Abstract

Keywords

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