Coarse geometry related to the coarse Baum-Connes conjecture
| Project/Area Number |
16K17595
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Ehime University |
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Principal Investigator |
Oguni Shin-ichi 愛媛大学, 理工学研究科(理学系), 教授 (00549446)
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| Project Period (FY) |
2016-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 粗Baum-Connes予想 / 粗凸距離空間 / 粗ホモトピー / 粗コンパクト化 / 双曲性 / 非正曲率性 / 粗幾何学 / 幾何学 |
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| Outline of Final Research Achievements |
We studied coarse geometry related to the coarse Baum-Connes conjecture. Also we studied geometric group theory which is deeply related to coarse geometry. Actually we introduced coarsely convex spaces and studied them with Tomohiro Fukaya (Tokyo metropolitan university). Also we introduced generalized Gromov products and studied them with Tomohiro Fukaya and Takamitsu Yamauchi (Ehime university). Also we studied acylindrical hyperbolicity of Artin-Tits groups with Motoko Kato (Ehime university).
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| Academic Significance and Societal Importance of the Research Achievements |
粗Baum-Connes予想に関わる粗幾何学について研究を進めた。粗Baum-Connes予想は、Novikov予想など微分トポロジーへの応用があるということ、および、ヒルベルト空間への粗埋め込み可能性や漸近次元の有限性などの粗幾何学における重要な性質の応用先であるということから、幾何学者やトポロジストを中心とした様々な研究者に興味を持たれている。粗幾何学は幾何学的群論とも深く関わり、この観点からの研究も進めた。本研究は粗幾何学にとどまらず、幾何学の進展に寄与するものであったと思われる。
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Report
(6 results)
Research Products
(18 results)
