geometry of automatic groups and dynamics of the boundary
| Project/Area Number |
23740049
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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 | Tohoku University (2012-2014)
Kyoto University (2011) |
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Principal Investigator |
FUKAYA TOMOHIRO 東北大学, 理学(系)研究科(研究院), 講師 (40583456)
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | Baum-Connes 予想 / 相対双曲群 / 境界 / 粗代数的位相幾何学 / 作用素環 / 粗Baum-Connes予想 / 非可換幾何学 / Coarse Geometry / Coarse Baum-Connes予想 / コンパクト化 / 国際情報交換（フランス，アメリカ） / 国際研究者交流 |
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| Outline of Final Research Achievements |
The Baum-Connes conjecture is one of the main topic of noncommutative geometry. We study its non-equivariant version, the coarse Baum-Connes conjecture. We proved that relatively hyperbolic groups satisfy the conjecture, under appropriate assumptions on parabolic subgroups. We also constructed a boundary for product of metric spaces. As application, we proved that the product of CAT(0)-groups, relatively hyperbolic groups, and polycyclic groups satisfy the conjecture.
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Report
(5 results)
Research Products
(18 results)
