2012 Fiscal Year Final Research Report
Volume Conjecture and its generalizations
| Project/Area Number |
22540069
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
MURAKAMI Hitoshi 東京工業大学, 大学院・理工学研究科, 准教授 (70192771)
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| Co-Investigator(Kenkyū-buntansha) |
HIKAMI Kazuhiro 九州大学, 数理(科)学研究科(研究院), 准教授 (60262151)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 位相幾何 / 結び目 / 体積予想 / Jones多項式 / 色付きJones多項式 / 体積 / Chern-Simons不変量 / Reidemeister torsion |
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| Research Abstract |
The volume conjecture states that by studying a certain asymptotic behavior of the colored Jones polynomial of a knot would tell us the volume of the knot complement. It was proposed by R. Kashaev, J. Murakami and the main investigator. Now the conjecture is generalized to various ways and attracts many researchers including theoretical physicists. In this research we solve part of the conjecture, give yet more generalizations, and solve part of these generalizations.
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