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.
|Number of pages||16|
|Journal||Algebraic and Geometric Topology|
|Publication status||Published - 1 Dec 2007|
- Cone manifolds
- Hyperbolic knot complements
- Hyperbolic link complements