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2015 Fiscal Year Final Research Report

Topological study of Riemann surfaces through infinite-dimensional Lie algebras

Research Project

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Project/Area Number 24340010
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
Section一般
Research Field Geometry
Research InstitutionThe University of Tokyo

Principal Investigator

Kawazumi Nariya  東京大学, 数理(科)学研究科(研究院), 准教授 (30214646)

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)
Project Period (FY) 2012-04-01 – 2016-03-31
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
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)

Free Research Field

位相幾何学

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Published: 2017-05-10  

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