The colored Jones polynomial and the A-polynomial of Knots
Copyright policy )The colored Jones polynomial and the A-polynomial of Knots
We study relationships between the colored Jones polynomial and the A-polynomial of a knot. We establish for a large class of 2-bridge knots the AJ conjecture (of Garoufalidis) that relates the colored Jones polynomial and the A-polynomial. Along the way we also calculate the Kauffman bracket skein module of all 2-bridge knots. Some properties of the colored Jones polynomial of alternating knots are established.
Typos and minor mistakes corrected. To appear in Advances in Mathematics
- Georgia Institute of Technology United States
- University of California, Berkeley United States
Mathematics(all), Two-bridge knots, AJ-conjecture, Geometric Topology (math.GT), A-polynomial, two-bridge knots, Invariants of knots and \(3\)-manifolds, Kauffman bracket skein module, Jones polynomial, Mathematics - Geometric Topology, Mathematics - Quantum Algebra, 57M25, AJ conjecture, FOS: Mathematics, Quantum Algebra (math.QA)
Mathematics(all), Two-bridge knots, AJ-conjecture, Geometric Topology (math.GT), A-polynomial, two-bridge knots, Invariants of knots and \(3\)-manifolds, Kauffman bracket skein module, Jones polynomial, Mathematics - Geometric Topology, Mathematics - Quantum Algebra, 57M25, AJ conjecture, FOS: Mathematics, Quantum Algebra (math.QA)
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