On the volume conjecture for hyperbolic knots
By Yoshiyuki Yokota. 2000
54 citations recorded by the source corpus.
In this article, we give a rough, and so not complete yet, proof of Kashaev's conjecture, that is, the volume conjecture for hyperbolic knots, where the hyperbolicity equations associated to knot diagrams appear as the stationary phase equations for Kashaev's invariants.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/aef23967b8dc08d57c9a93c01fa9bc4b2c7023e4
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- ASYMPTOTICS OF THE QUANTUM INVARIANTS FOR SURGERIES ON THE FIGURE 8 KNOT (2005, unknown): “Therefore m ∏ l=0 (1 − ξk−l) = Sγ(−π + 2γ(k −m)− γ) Sγ(−π + 2γk + γ) , m ∏ l=0 (1 − ξk+l) = Sγ(−π + 2γk − γ) Sγ(−π + 2γ(k +m) + γ) .”
- Colored Alexander invariants and cone-manifolds (2008, methodology): “A-polynomials In this section, we introduce a polynomial or a system of polynomials of the above three examples by using the method in [13].”
- The colored Jones polynomials of the figure-eight knot and its Dehn surgery spaces (2004, unknown): “Then 2π lim N→∞ log JN ( K; exp(2π √ −1/N) ) N = Vol(S3 \K) + √ −1CS(S3 \K), where Vol is the hyperbolic volume and CS is the Chern–Simons invariant for knots [7].”