On the volume conjecture for hyperbolic knots
Yoshiyuki Yokota
TL;DR
This paper provides a partial proof of Kashaev's volume conjecture for hyperbolic knots, linking hyperbolicity equations to stationary phase equations of knot invariants.
Contribution
It offers a rough, not yet complete, proof of the volume conjecture connecting hyperbolic geometry and quantum invariants of knots.
Findings
Partial validation of the volume conjecture for hyperbolic knots
Identification of hyperbolicity equations as stationary phase equations
Progress towards a complete proof of Kashaev's conjecture
Abstract
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.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory