un 2 00 7 DEHN FILLING , VOLUME , AND THE JONES POLYNOMIAL
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چکیده
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.
منابع مشابه
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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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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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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Given a knot in 3-space, one can associate a sequence of Laurrent polynomials, whose nth term is the nth colored Jones polynomial. The Generalized Volume Conjecture states that the value of the n-th colored Jones polynomial at exp(2πiα/n) is a sequence of complex numbers that grows exponentially, for a fixed real angle α. Moreover the exponential growth rate of this sequence is proportional to ...
متن کاملThe Colored Jones Polynomials and the Alexander Polynomial of the Figure-eight Knot
Abstract. The volume conjecture and its generalization state that the series of certain evaluations of the colored Jones polynomials of a knot would grow exponentially and its growth rate would be related to the volume of a threemanifold obtained by Dehn surgery along the knot. In this paper, we show that for the figure-eight knot the series converges in some cases and the limit equals the inve...
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تاریخ انتشار 2006