| Project/Area Number |
18540086
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Okayama University |
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Principal Investigator |
MORIMOTO Masaharu Okayama University, 大学院・自然科学研究科, 教授 (30166441)
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| Co-Investigator(Kenkyū-buntansha) |
NAKAJIMA Atsushi 岡山大学, 大学院・自然科学研究科, 名誉教授 (30032824)
IKEHATA Shuichi 岡山大学, 大学院・自然科学研究科, 教授 (20116429)
SHIMAKAWA Kazuhisa 岡山大学, 大学院・自然科学研究科, 教授 (70109081)
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| Project Period (FY) |
2006 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥4,220,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥720,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | 微分トポロジー / 変換群 / 多様体 / 球面上の作用 / Smith問題 / Laitinen予想 / 球面 / 群作用 / 不動点 / 接空間表現 / Oliver群 / gap群 / Smith 問題 / Laitinen 予想 / 球面上の群作用 / Oliver 群 / 有限群の作用 / 接空間 / Smith同値 / 実表現 / Laitien予想 |
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| Research Abstract |
For a finite group G, the subset of real representation ring consisting of all differences of tangential representations at fixed points of smooth G-actions with exactly two fixed points on spheres is called the Smith set of G. In this research, we computed the Smith sets for many finite groups G.Furthermore, we found counterexamples to Laitinen's Conjecture on the Smith sets as well as a family of finite groups for which the conjecture is valid, which contributed to development of the study of Smith's problem.
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