Proof of Volume Conjecture for twist knots
Sukuse Abe
TL;DR
This paper proves the volume conjecture for all twist knots using complex analysis, analytic continuation, and colored Jones polynomials, establishing a significant link between knot invariants and hyperbolic volume.
Contribution
It provides a complete proof of the volume conjecture specifically for twist knots, employing advanced mathematical techniques.
Findings
Confirmed the volume conjecture for all twist knots
Established a new method using complex analysis and analytic continuation
Linked colored Jones polynomials to hyperbolic volume for twist knots
Abstract
We prove the volume conjecture for any twist knots by using an equivalence relation, complex analysis, analytic continuation, and function of several complex variables on the basis of colored Jones polynomials.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology