The volume conjecture for augmented knotted trivalent graphs

van der Veen, Roland

doi:10.2140/agt.2009.9.691

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The volume conjecture for augmented knotted trivalent graphs

Roland van der Veen

Algebraic & Geometric Topology 9 (2009) 691–722

DOI: 10.2140/agt.2009.9.691

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

References

Publication

Received: 5 February 2009

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

Volume 9, issue 2 (2009)