Volumes of highly twisted knots and links

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15 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 languageEnglish
Pages (from-to)93-108
Number of pages16
JournalAlgebraic and Geometric Topology
Volume7
Issue number1
DOIs
Publication statusPublished - 1 Dec 2007
Externally publishedYes

Keywords

  • Cone manifolds
  • Hyperbolic knot complements
  • Hyperbolic link complements
  • Volume

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