Dehn filling, volume, and the Jones polynomial

Details Dehn filling, volume, and the Jones polynomial Dehn filling, volume, and the Jones polynomial

2006-12-06

arxiv.org/abs/math/0612138v4

Journal of Differential Geometry 78 (2008), no 3, 429-464

Mathematics

Geometric Topology

This version contains corrections to Section 4. Published in Journal of Differential Geometry

Scientific paper

Given a hyperbolic 3-manifold with torus boundary, we bound the change in volume under a Dehn filling where all slopes have length at least 2\pi. This result is applied to give explicit diagrammatic bounds on the volumes of many knots and links, as well as their Dehn fillings and branched covers. Finally, we use this result to bound the volumes of knots in terms of the coefficients of their Jones polynomials.

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