| Project/Area Number |
15K17528
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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 | Tokyo Metropolitan University (2016-2018)
Tohoku University (2015) |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 粗幾何学 / coarse geometry / coarse Baum-Connes予想 / coarsely convex space / coares Baum-Connes / nonpositive curvature / Cartan-Hadamard theorem / 粗Cartan-Hadaramの定理 / 粗凸空間 / 粗Baum-Connes予想 / Coarse Geometry / non-positively curved / Coarse Baum-Connes予想 / 相対双曲群 |
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| Outline of Final Research Achievements |
We introduced a new class of metric spaces, called "coarsely convex spaces", which is a generalization of Riemannian manifolds of nonpositive sectional curvatures. This class is closed under both quasi-isometry and direct products. We constructed boundaries of the coarsely convex spaces and we established a coarse version of the Cartan-Hadamard theorem. Using this, we proved that the coarsely convex spaces satisfy the coarse Baum-Connes conjecture.
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| Academic Significance and Societal Importance of the Research Achievements |
粗Baum-Connes予想は非可換幾何学及び距離空間の粗幾何学に於ける中心的な問題である．私達は粗凸空間という，非正曲率を持つ距離空間の新しい定式化を導入し，その空間に対して粗Baum-Connes予想が成り立つことを示した．近年，粗凸空間に幾何学的な作用を持つ様々な群が発見されている．私達の結果から，こうした群に対して粗Baum-Connes予想が成立することが従う．
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