Development and Applications of Arithmetic Topology
| Project/Area Number |
21340010
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kyushu University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
河野 俊丈 東京大学, 数理科学研究科, 教授
栗原 将人 慶応義塾大学, 理工学部, 教授
坂内 健一 慶応義塾大学, 理工学部, 講師
田口 雄一郎 九州大学, 数理学研究院, 准教授
寺嶋 郁二 東京工業大学, 理工学研究科, 助教
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥6,110,000 (Direct Cost: ¥4,700,000、Indirect Cost: ¥1,410,000)
Fiscal Year 2011: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2010: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2009: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
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| Keywords | 結び目 / 素数 / 数論的位相幾何学 |
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| Research Abstract |
Based on the analogies between knots and primes, I found a new branch of mathematics, called arithmetic topology, focused upon the analogies between knot theory and number theory. I wrote a book giving a foundation of this field. As applications, I studied some analogies between 3-dimensional hyperbolic geometry, Chern-Simons theory and Hida theory. I also organized international workshops,“Low dimensional topology and number theory", every year during 2009. 2012.
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Report
(4 results)
Research Products
(26 results)
