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2007 Volumes of highly twisted knots and links
Jessica Purcell
Algebr. Geom. Topol. 7(1): 93-108 (2007). DOI: 10.2140/agt.2007.7.93

Abstract

We show that for a large class of knots and links with complements in S3 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.

Citation

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Jessica Purcell. "Volumes of highly twisted knots and links." Algebr. Geom. Topol. 7 (1) 93 - 108, 2007. https://doi.org/10.2140/agt.2007.7.93

Information

Received: 21 April 2006; Revised: 3 January 2007; Accepted: 3 January 2007; Published: 2007
First available in Project Euclid: 20 December 2017

zbMATH: 1135.57005
MathSciNet: MR2289805
Digital Object Identifier: 10.2140/agt.2007.7.93

Subjects:
Primary: 57M25, 57M50

Rights: Copyright © 2007 Mathematical Sciences Publishers

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