The Colored Jones Polynomial and the Volume Conjecture

Geometry Topology Student Seminar
Wednesday, October 29, 2014 - 14:00
1 hour (actually 50 minutes)
Skiles 006
Georgia Tech

This is a project for Prof. Margalit's course on Low-dimensional Topology and Hyperbolic Geometry.

We will present an introduction to the notion of quantum invariants of knots and links, and in particular the colored Jones polynomial. We will also introduce the Volume Conjecture, which relates a certain limiting behavior of a quantum invariant (the colored Jones polynomial of a link) with a classical invariant (the hyperbolic volume of the hyperbolic part of a link complement in S^3) and has been proven in a number of cases.