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Journal of the London Mathematical Society Advance Access originally published online on July 25, 2007
Journal of the London Mathematical Society 2007 76(1):1-15; 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

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.

costanti{at}math.u-strasbg.fr

2000 Mathematics Subject Classification 57M27 (primary), 57M50 (secondary).

Received October 12, 2005; revised August 8, 2006; published online July 25, 2007.


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