Dehn filling, volume, and the Jones polynomial

David Futer, Efstratia Kalfagianni, Jessica S. Purcell

Published 2006-12-06, updated 2008-02-13Version 4

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.