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On the Generalized Hyperbolic Volume Conjecture
by
Stavros Garoufalidis
Georgia Tech
Coauthors: Thang Le
The Generalized Hyperbolic Volume Conjecture (GHVC) states that the n-th colored Jones polynomial, evaluated at exp(2 pi i a/n), is a sequence of complex numbers that grows exponentially. Moroever, the exponential growth rate is proportional to the volume of the corresponding Dehn filling. We prove two statements: (a) the limsup in the GHVC is finite for all knots and all a. (b) for every knot K there exists a positive angle a(K) such that the GHVC holds for a in [0, a(K)). The proofs of these statements use elementary properties of state sum formulas for the colored Jones polynomial, and its recursion and its cyclotomic expansion. Viva Lou!
Date received: January 19, 2005
Copyright © 2005 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # capo-05.