Quantum knot invariants

  • Stavros Garoufalidis
Part of the following topical collections:
  1. Modular Forms are Everywhere: Celebration of Don Zagier’s 65th Birthday


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.


Jones polynomial Knots Quantum topology Volume conjecture Nahm sums Stability Modularity Modular forms Mock-modular forms q-Holonomic sequence q-Series 

Mathematics Subject Classification

Primary 57N10 Secondary 57M25 



The author was supported in part by NSF. To Don Zagier, with admiration.

Ethics approval and consent to participate

Not applicable.


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Authors and Affiliations

  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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