Algebraic & Geometric Topology

Volumes of highly twisted knots and links

Jessica Purcell

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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.

Article information

Source
Algebr. Geom. Topol., Volume 7, Number 1 (2007), 93-108.

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796660

Digital Object Identifier
doi:10.2140/agt.2007.7.93

Mathematical Reviews number (MathSciNet)
MR2289805

Zentralblatt MATH identifier
1135.57005

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M50: Geometric structures on low-dimensional manifolds

Keywords
hyperbolic knot complements hyperbolic link complements volume cone manifolds

Citation

Purcell, Jessica. Volumes of highly twisted knots and links. Algebr. Geom. Topol. 7 (2007), no. 1, 93--108. doi:10.2140/agt.2007.7.93. https://projecteuclid.org/euclid.agt/1513796660


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