Topological study of Riemann surfaces through infinite-dimensional Lie algebras
| Project/Area Number |
24340010
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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 | The University of Tokyo |
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Principal Investigator |
Kawazumi Nariya 東京大学, 数理(科)学研究科(研究院), 准教授 (30214646)
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| Co-Investigator(Renkei-kenkyūsha) |
TADOKORO Yuuki 木更津工業高等専門学校, 准教授 (10435414)
SATOH Takao 東京理科大学, 理学部第二部, 准教授 (70533256)
SATO Masatoshi 東京電機大学, 未来科学部, 准教授 (10632010)
KUNO Yusuke 津田塾大学, 学芸学部, 准教授 (80632760)
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥17,550,000 (Direct Cost: ¥13,500,000、Indirect Cost: ¥4,050,000)
Fiscal Year 2014: ¥6,890,000 (Direct Cost: ¥5,300,000、Indirect Cost: ¥1,590,000)
Fiscal Year 2013: ¥6,760,000 (Direct Cost: ¥5,200,000、Indirect Cost: ¥1,560,000)
Fiscal Year 2012: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
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| Keywords | リーマン面 / ゴールドマン・リー代数 / 写像類群 / 正則ホモトピー / トゥラエフ余括弧積 / 榎本佐藤トレース / 発散コサイクル / 無限次元リー代数 / ゴールドマン・トゥラエフ・リー双代数 / トポロジー / マグナス展開 / ジョンソン準同型 / 榎本-佐藤トレース / ファットグラフ / 形式的シンプレクティック幾何学 / ホモロジカル・ゴールドマン・リー代数 |
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| Outline of Final Research Achievements |
We introduced a new regular homotopy version of the Goldman-Turaev Lie bialgebra, where null-homotopic loops are reserved. This lead us a new close relationship among the Goldman-Turaev Lie bialgebra, the Enomoto-Satoh trace and the Kashiwara-Vergne problem. (Kawazumi)
We gave a tensorial description of the completed Goldman Lie algebra of a compact connected surface with non-empty boundary. As colloraries, we obrained ``the infinitesimal Dehn-Nielsen theorem” and a geometric formulation of the Johnson homomorphisms in the case where the boundary is not connected.(Kawazumi-Kuno)
We showed that the homological Goldman Lie algebra is finitely generated, and that the smallest number of its generating system is 2g+2.(Kawazumi-Kuno-Toda)
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Report
(5 results)
Research Products
(36 results)
