2009 Fiscal Year Final Research Report
Geometry and Invariants of 3-manifolds
| Project/Area Number |
18204004
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
KOJIMA Sadayoshi Tokyo Institute of Technology, 大学院・情報理工学研究科, 教授 (90117705)
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| Co-Investigator(Kenkyū-buntansha) |
YOSHIDA Tomoyoshi 東京工業大学, 大学院・理学研究科, 教授 (60055324)
MORITA Shigeyuki 東京大学, 大学院・数理科学研究科, 教授 (70011674)
MATSUMOTO Shigenori 日本大学, 理工学部, 教授 (80060143)
SOMA Teruhiko 首都大学東京, 大学院・理工学研究科, 教授 (50154688)
FUJIWARA Koji 東北大学, 大学院・情報科学研究科, 教授 (60229078)
OHTSUKI Tomotada 京都大学, 数理解析研究所, 准教授 (50223871)
TAKASAWA Mitsuhiko 東京工業大学, 大学院・情報理工学研究科, 助教 (80323822)
KUMAGAI Takashi 京都大学, 大学院・理学研究科, 教授 (90234509)
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| Project Period (FY) |
2006 – 2009
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| Keywords | 位相幾何 / 3次元トポロジー / 双曲幾何 / 幾何構造 / 位相不変量 / 体積 |
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| Research Abstract |
We have studied the interaction between geometric structures and invariants of 3-manifolds in order to get deeper understanding for their topology, and obtained several new results on global behavior of geometric invariants. In particular, the reporter attained a few progress on comparison of dynamical invariants of mapping classes of a surface and simplicial volumes of their mapping tori. Also, we have organized an international conference to review our activities in the last year, and pointed out many issues that suggest further direction.
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