Study of the mapping class group using the intersections of curves on surfaces
| Project/Area Number |
26800044
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Tsuda University |
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Principal Investigator |
Kuno Yusuke 津田塾大学, 学芸学部, 准教授 (80632760)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 写像類群 / ゴールドマン括弧積 / テュラエフ余括弧積 / ジョンソン準同型 / トュラエフ余括弧積 / デーンツイスト / 位相幾何学 |
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| Outline of Final Research Achievements |
The main object of this research project was the Turaev cobracket which is a topological operation measuring the self-intersections of curves on surfaces. In particular, we studied the relationship between the Kashiwara-Vergne problem in Lie theory and the Turaev cobracket. As a result, we established the formality property of the Turaev cobracket and obtained its application to the theory of the Johnson homomorphisms.
We also studied generalized Dehn twists, which is a certain algebraic construction associated to any closed curves on surfaces. In particular, we tried to clarify a geometric interpretation of generalized Dehn twists and partially succeeded in the sense that we obtained a first approximation of them in terms of homology cylinders.
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Report
(5 results)
Research Products
(34 results)
