An Introduction to the Volume Conjecture

By Hitoshi Murakami. 2010

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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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/9224c503f1ebd6c0724e083cbbdb1bfae6d024e9