#### Volume 9, issue 2 (2009)

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The volume conjecture for augmented knotted trivalent graphs

### Roland van der Veen

Algebraic & Geometric Topology 9 (2009) 691–722
##### Abstract

We propose to generalize the volume conjecture to knotted trivalent graphs and we prove the conjecture for all augmented knotted trivalent graphs. As a corollary we find that for any link $L$ there is an arithmetic link containing $L$ for which the volume conjecture holds.

##### Keywords
volume conjecture, Jones polynomial, Kashaev invariant, knotted trivalent graph, augmented, knot complement, hyperbolic volume, graph complement, graph invariant, octahedra, hyperbolic, 6j symbol, skein theory
##### Mathematical Subject Classification 2000
Primary: 57M25, 57M27
##### Publication
Revised: 4 March 2009
Accepted: 11 March 2009
Published: 9 April 2009
##### Authors
 Roland van der Veen KdV Institute for Mathematics University of Amsterdam Plantage Muidergracht 24 1018 TV Amsterdam The Netherlands http://www.science.uva.nl/~riveen