Dehn filling, volume, and the Jones polynomial

Dehn Filling, Volume, and the Jones Polynomial

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...

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un 2 00 7 DEHN FILLING , VOLUME , AND THE JONES POLYNOMIAL

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...

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Se p 20 07 DEHN FILLING , VOLUME , AND THE JONES POLYNOMIAL

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...

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Reducing Dehn filling and toroidal Dehn filling

It is shown that if M is a compact, connected, orientable hyperbolic 3-manifold whose boundary is a torus, and 7‘1, FZ are two slopes on i7M whose associated fillings are respectively a reducible manifold and one containing an essential torus, then the distance between these slopes is bounded above by 4. Under additional hypotheses this bound is improved Consequently the cabling conjecture is s...

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Exceptional Dehn filling

This Research in Team workshop focused on several problems in the theory of exceptional Dehn fillings in 3dimensional topology. Dehn filling is the construction in which you take a 3-manifoldM , with a distinguished torus boundary component T , and glue a solid torus V to M via some homeomorphism from ∂V to T . The resulting manifold depends only on the isotopy class (slope) α on T that is iden...

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Dehn filling, volume, and the Jones polynomial

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