Studies on rational visibility problems of a Lie Group and extensions of symplectic classes by a model for the evaluation map
| Project/Area Number |
20540070
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Shinshu University |
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Principal Investigator |
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| Project Period (FY) |
2008 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | サリバンモデル / c-シンプレクティック多様体 / 写像空間 / 特性類 / シンプレクティック多様体 / Sullivanモデル / sullivanモデル / 幾何学 / トポロジー / 写像空間モデル / スペクトル系列 / 有理ホモトピー論 / 有理モデル / 可視化問題 |
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| Research Abstract |
We have solved the rational visibility problems of simple Lie groups which give homogeneous spaces of rank one. In particular, the visible degrees are determined explicitly for all the cases of such Lie groups. Moreover, for a fibration with symplectic fibre, we discuss a necessary and sufficient condition for the cohomology class of the symplectic form to extend to a cohomology class of the total space of the fibration provided the 2k-dimensional torus is rationally separable from the fibre. Our main tools for the study are the Sullivan model for a function space due to Brown and Szczarba and a rational model for the evaluation map.
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Report
(6 results)
Research Products
(14 results)
