Volumes of highly twisted knots and links

Abstract

We show that for a large class of hyperbolic knots and links, 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.

14 pages, 4 figures. Minor changes to clarify exposition, fix typos, and correct a historical inaccuracy in the introduction. Paper has now appeared in AGT

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