| Project/Area Number |
20740033
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
YOSHINO Taro Tokyo Institute of Technology, 大学院・理工学研究科, 助教 (20447890)
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 非リーマン等質空間 / 不連続群 / Clifford-Klein形 / 位相的ブローアップ / 変形空間 / 非ハウスドルフ空間 / Lipsman予想の反例 / Lipsman予想 / 幾何学 |
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| Research Abstract |
At first, I had planed to calculate deformation spaces of Clifford-Klein forms. However, I found that such deformation spaces are non-Hausdorff in many cases, and it is not easy to get an intuition of the deformation space.
In order to understand such non-Hausdorff spaces, I have introduced a method topological blow-up'. This method is similar to the blow-up for algebraic varieties. Applying this method for a non-Hausdorff space, we obtain a Hausdorff space. This Hausdorff space has much information about the topology of the original non-Hausdorff space. Especially, if we apply it for deformation spaces of Clifford-Klein forms, we can obtain complete information on the topology of the deformation space from the blow-upped spaces.
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