2012•arXiv (Cornell University)Open access

Quantum Knot Invariants

Stavros Garoufalidis

Abstract

This is a survey talk on one of the best known quantum knot invariants, the colored Jones polynomial of a knot, and its relation to the algebraic/geometric topology and hyperbolic geometry of the knot complement. We review several aspects of the colored Jones polynomial, emphasizing modularity, stability and effective computations. The talk was given in the Mathematische Arbeitstagung June 24-July 1, 2011. Updated the bibliography.

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Key concepts: Quantum invariant, Jones polynomial, Knot polynomial, Knot invariant, Colored, Trefoil knot, Knot (papermaking), Knot theory