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Journal of the London Mathematical Society Advance Access first published online on July 25, 2007
This version published online on September 19, 2007
Journal of the London Mathematical Society, doi:10.1112/jlms/jdm029
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© 2007 London Mathematical Society

Coloured Jones invariants of links and the volume conjecture

Francesco Costantino

Institut de Recherche Mathématique Avancée (IRMA)
7 Rue René Descartes
67084 Strasbourg Cedex
France
costanti{at}math.u-strasbg.fr

We extend the definition of the coloured Jones polynomials to framed links and trivalent graphs in S3#k(S2 x S1) using a state-sum formulation based on Turaev's shadows. Then, we prove that the natural extension of the Volume Conjecture holds true for an infinite family of hyperbolic links.

The original version of this paper was published in error before the proofs had been corrected.

Received October 12, 2005; revised August 8, 2006;
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