Quantum invariants of knots and representations of knot groups

2016 Fiscal Year Final Research Report

• Project/Area Number: 26400079
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Tohoku University
• Principal Investigator: Murakami Hitoshi 東北大学, 情報科学研究科, 教授 (70192771)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 体積予想 / Jons多項式 / 結び目 / Chern-Simons不変量 / Reidemeister torsion

Outline of Final Research Achievements

In this research I studied mainly on the volume conjecture and its generalization about the colored Jones polynomial of a knot.
As a result, I proved a generalization of the volume conjecture, that is, I proved that the asymptotic behavior of the colored Jones polynomial gives the Chern-Simons invariant and the Reidemeister torsion of the knot complement.

Free Research Field

結び目理論