Colored Jones invariants of links in S^3 # k S^2 X S^1 and the Volume Conjecture

Details Colored Jones invariants of links in S^3 # k S^2 X S^1 and the Volume Conjecture Colored Jones invariants of links in S^3 # k S^2 X S^1 and the Volume Conjecture

2005-10-03

arxiv.org/abs/math/0510048v2

Mathematics

Geometric Topology

15 pages, 6 figures

Scientific paper

We extend the definition of the colored Jones polynomials to framed links and
trivalent graphs in S^3 # k S^2 X S^1 using a state-sum formulation based on
Turaev's shadows. Then, we prove that the natural extension of the Volume
Conjecture is true for an infinite family of hyperbolic links.

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