2013 Fiscal Year Final Research Report
Study of problems on discrete groups by geometric methods
| Project/Area Number |
21340014
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Nagoya University |
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Principal Investigator |
NAYATANI Shin 名古屋大学, 多元数理科学研究科, 教授 (70222180)
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| Co-Investigator(Renkei-kenkyūsha) |
KANAI Masahiko 東京大学, 大学院・数理科学研究科, 教授 (70183035)
KOTANI Motoko 東北大学, 大学院・理学研究科, 教授 (50230024)
NAITO Hisashi 名古屋大学, 多元数理科学研究科, 准教授 (40211411)
IZEKI Hiroyasu 慶応義塾大学, 理工学部, 教授 (90244409)
KAMADA Hiroyuki 宮城教育大学, 教育学部, 教授 (00249799)
KOBAYASHI Toshimasa 摂南大学, 工学部, 講師 (30399125)
ITO Kentaro 名古屋大学, 多元数理科学研究科, 准教授 (00324400)
KONDO Takefumi 神戸大学, 理学研究科, GCOE博士研究員 (60467446)
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| Project Period (FY) |
2009-04-01 – 2014-03-31
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| Keywords | 固定点性質 / CAT(0)空間 / ランダム群 / 不変量δ / 非線形スペクトルギャップ |
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| Research Abstract |
We proved that Gromov's group containing quasi-isometric image of expanders has fixed-point property for a large class of CAT(0) spaces. In relation to the possible geometric proof of the Margulis superrigidity theorem, we studied a certain geometric invariant of the 2-dimensional Euclidean building associated to PGL(3,Q_p). In the case p=2, we made progress on the related deformation problem of polyhedral. Motivated by a certain rigidity problem on discrete groups, we studied conformal-geometric structures such as strongly pseudoconvex CR structures and quaternionic CR structures, and obtained some results.
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