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