Topology of knots and 3-manifolds
| Project/Area Number |
24340012
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
谷山 公規 早稲田大学, 教育・総合科学学術院, 教授 (10247207)
平澤 美可三 名古屋工業大学, 工学(系)研究科(研究院), 教授 (00337908)
大山 淑之 東京女子大学, 公私立大学の部局等, 教授 (80223981)
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| Co-Investigator(Renkei-kenkyūsha) |
KAMADA Seiichi 大阪市立大学, 理学研究科, 教授 (60254380)
HABIRO Kazuo 京都大学, 数理解析研究所, 准教授 (80346064)
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| Project Period (FY) |
2012-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥10,270,000 (Direct Cost: ¥7,900,000、Indirect Cost: ¥2,370,000)
Fiscal Year 2015: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2014: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2013: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2012: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
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| Keywords | 結び目 / ３次元多様体 / 不変量 / 低次元トポロジー / 量子トポロジー / 3次元多様体 |
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| Outline of Final Research Achievements |
The author calculated the asymptotic expansion of the Kashaev invariant for some hyperbolic knots, and proved the volume conjecture for these knots. Further, the author proved "the volume conjecture for 3-manifolds" for hyperbolic 3-manifolds obtained by integral surgery along the figure-eight knot.
The author held the workshop "Intelligence of Low-dimensional Topology" at RIMS in each year. Further, the author held the topology symposium in 2014 and 2015. Furthermore, Taniyama, Motegi and Ohyama held the workshop "Musubime no Sugaku (Mathematics of Knots)" in each year.
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Report
(6 results)
Research Products
(62 results)
