An Introduction to the Volume Conjecture

Details An Introduction to the Volume Conjecture An Introduction to the Volume Conjecture

2010-01-31

arxiv.org/abs/1002.0126v1

Mathematics

Geometric Topology

39 pages, 37 figures, submitted to the proceedings of the workshop "Interactions Between Hyperbolic Geometry, Quantum Topology

Scientific paper

This is an introduction to the Volume Conjecture and its generalizations for nonexperts. The Volume Conjecture states that a certain limit of the colored Jones polynomial of a knot would give the volume of its complement. If we deform the parameter of the colored Jones polynomial we also conjecture that it would also give the volume and the Chern-Simons invariant of a three-manifold obtained by Dehn surgery determined by the parameter. I start with a definition of the colored Jones polynomial and include elementary examples and short description of elementary hyperbolic geometry.

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