An Introduction to the Volume Conjecture

Understand

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.