Volumes of highly twisted knots and links

Jessica Purcell

doi:10.2140/agt.2007.7.93

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Home > Journals > Algebr. Geom. Topol. > Volume 7 > Issue 1 > Article

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

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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.