| Project/Area Number |
21K03243
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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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| Review Section |
Basic Section 11020:Geometry-related
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| Research Institution | The University of Tokyo |
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Principal Investigator |
Kanai Masahiko 東京大学, 大学院数理科学研究科, 名誉教授 (70183035)
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| Project Period (FY) |
2021-04-01 – 2024-03-31
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| Project Status |
Completed (Fiscal Year 2023)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2023: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2022: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2021: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | トンプソン群 / 群作用 / ファレイ図式 / Thompson 群 / 自己同型 |
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| Outline of Research at the Start |
トンプソン群の背後に存在することが期待される空間やその上の構造を探索する．
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| Outline of Final Research Achievements |
As spaces on which the Thompson group F acts, we constructed the following ones: (I) The Dedekind-MacNeille completion of some lattice-ordered group; (II) A domain in some infinite-dimensional affine space; (III) A domain in some infinite simensional sphere. As an application of (I), we gave an alernative proof of the theorem of McCleary-Rubin.
Meanwhile, as to (II), we determined a fundamental domain, and constructed an invariant measure. In addition, we made considerations which arise from the piecewise integral projective realization of the Thompson group T.
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| Academic Significance and Societal Importance of the Research Achievements |
現時点までに得られた成果は，残念ながらさして満足のいくものではないというのが正直なところである．しかし，この方向に研究を続けていけば，近い将来大きな成果をあげられると期待している．とくに，トンプソン群が作用する空間の上で調和積分論を展開することができれば，数学に大きな進展をもたらすであろう．
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