#### Volume 7, issue 1 (2007)

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Volumes of highly twisted knots and links

### Jessica S Purcell

Algebraic & Geometric Topology 7 (2007) 93–108
 arXiv: math.GT/0604476
##### 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.

##### Keywords
hyperbolic knot complements, hyperbolic link complements, volume, cone manifolds
##### Mathematical Subject Classification 2000
Primary: 57M25, 57M50