Quantum invariants of knots and representations of knot groups
| Project/Area Number |
26400079
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Tohoku University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
樋上 和弘 九州大学, 数理学研究院, 准教授 (60262151)
藤 博之 香川大学, 教育学部, 准教授 (50391719)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 体積予想 / Jons多項式 / 結び目 / Chern-Simons不変量 / Reidemeister torsion / 量子位相幾何学 / 低次元位相幾何学 / 色付きJones多項式 / torus 結び目 / Chern-Simons 不変量 / 基本群の表現 / トーラス結び目 / ジョーンズ多項式 / チャーン・サイモンズ不変量 / ライデマイスターの捩れ |
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| 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.
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Report
(4 results)
Research Products
(34 results)
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[Journal Article] Partial chord diagrams and matrix models2017
Author(s)
J. E. Andersen, H. Fuji, M. Manabe, R. C . Penner, and P. Sulkowski
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Journal Title
Travaux Mathematiques, University of Luxembourg
Volume: 25
Pages: 233-283
Related Report
Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
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