Topological studies on mapping class groups of knotted surafces and 3-dimensional handlebodies
| Project/Area Number |
24540096
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Tokyo University of Science |
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Principal Investigator |
Hirose Susumu 東京理科大学, 理工学部, 教授 (10264144)
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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 |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 位相幾何学 / 低次元トポロジー / 写像類群 / 曲面結び目 / ３次元ハンドル体 / リーマン面 / 3次元ハンドル体 / 周期的写像 / 擬アノソフ同相写像 / 組み紐群 / 向き付け不可能閉曲面 / トレリ群 / Morse-Smale 流 / ジョンソン準同型 |
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| Outline of Final Research Achievements |
We made several researches mainly on the mapping class group related to topology on the surface embedded in 3 or 4-manifolds. Especially, we obtained results on the abelianization and minimal generating set of the level 2 mapping class groups of non-orientable surfaces, a normal generating set of the Torelli groups of non-orientable surfaces, pseudo-Anosov elements and finite presentations of the hyper-elliptic handlebody group, links which are closed orbits of Morse-Smale flows on the 3-sphere, a uniqueness and periods of null-cobordant periodic maps on closed orientable surfaces, and a uniqueness of periodic maps on compact surfaces with boundaries.
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Report
(5 results)
Research Products
(19 results)
