Journal of Differential Geometry

Dehn filling, volume, and the Jones polynomial

D. Futer, E. Kalfagianni, and J. Purcel

Full-text: Open access

Abstract

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.

Article information

Source
J. Differential Geom. Volume 78, Number 3 (2008), 429-464.

Dates
First available in Project Euclid: 10 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1207834551

Digital Object Identifier
doi:10.4310/jdg/1207834551

Mathematical Reviews number (MathSciNet)
MR2396249

Zentralblatt MATH identifier
1144.57014

Citation

Futer, D.; Kalfagianni, E.; Purcel, J. Dehn filling, volume, and the Jones polynomial. J. Differential Geom. 78 (2008), no. 3, 429--464. doi:10.4310/jdg/1207834551. https://projecteuclid.org/euclid.jdg/1207834551


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