Hitoshi Murakami
Published 2010-01-31Version 1
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.
Comments: 39 pages, 37 figures, submitted to the proceedings of the workshop "Interactions Between Hyperbolic Geometry, Quantum Topology and Number Theory"
The colored Jones polynomial, the Chern--Simons invariant, and the Reidemeister torsion of the figure-eight knot
Representations and the colored Jones polynomial of a torus knot
Turaev-Viro invariants, colored Jones polynomials and volume
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