Dehn filling, volume, and the Jones polynomial

David Futer, Efstratia Kalfagianni, Jessica S. Purcell

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81 Citations (Scopus)


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 2π. 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.

Original languageEnglish
Pages (from-to)429-464
Number of pages36
JournalJournal of Differential Geometry
Issue number3
Publication statusPublished - 1 Jan 2008
Externally publishedYes

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