Quantum Knot Invariants
arXiv:1201.3314
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.
17 pages, 13 figures, Arbeitstagung talk Bonn 2011
References in corpus (9)
- On the characteristic and deformation varieties of a knot
- 3-Manifolds and 3d Indices
- SL(2,C) Chern-Simons theory and the asymptotic behavior of the colored Jones polynomial
- Rogers-Ramanujan type identities and the head and tail of the colored Jones polynomial
- Slopes and colored Jones polynomials of adequate knots
- Chern-Simons theory, analytic continuation and arithmetic
- On the AJ conjecture for knots
- Nahm sums, stability and the colored Jones polynomial
- Twisting q-holonomic sequences by complex roots of unity